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ISSN: 2475-4811 (print)

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Volume 9 (2025)

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Volume 8 (2024)

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Volume 7 (2023)

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Volume 5 (2021)

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Volume 4 (2020)

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Volume 3 (2019)

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Volume 2 (2018)

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Volume 1 (2017)

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Journal of Vibration Testing and System Dynamics

JVTSD Volume 1, Issue 1

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The Use of the Fitting Time HistoriesMethod to Detect the Nonlinear Behaviour of Laminated Glass

pp. 1-14 | DOI: 10.5890/JVTSD.2017.03.001

S. Lenci†, L. Consolini, F. Clementi

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Abstract

The experimental free vibrations of a laminated glass beam are inves- tigated with the aim of extracting the nonlinear characteristics of the dynamical behaviour, by an appropriate post-processing of data en- suing from the tests. An updated version of the Fitting Time History (FTH) technique is used. It is based on the least square approx- imation of the measured damped free vibrations of the laminated glass, and provides the optimal values of the natural frequencies and damping coefficients. While in a previous work attention was mainly devoted to the determination of the linear dynamical properties, here the focus is on the nonlinear behaviour, in particular on the nonlinear relationship between the excitation amplitude and: (i) the natural frequencies, a fact that is commonly encountered in nonlinear dy- namics and known as ‘backbone curve’; (ii) the damping coefficient, a fact that is somehow unexpected and commonly not reported in the literature.

Dynamics of Turning Operation Part I: Experimental Analysis Using Instantaneous Frequency

pp. 15-33 | DOI: 10.5890/JVTSD.2017.03.002

Eric B. Halfmann, C. Steve Suh, Wayne N.P. Hung

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Abstract

The workpiece and tool vibrations on a lathe are experimentally stud- ied to establish improved understanding of cutting dynamics that would support efforts in exceeding the current limits of the turning process. A Keyence laser displacement sensor is employed to monitor the workpiece and tool vibrations during chatter-free and chatter cut- ting. A procedure is developed that utilizes instantaneous frequency (IF) to identify the modes related to measurement noise and those innate of the cutting process. It is found that IF thoroughly charac- terizes the underlying turning dynamics and identifies the exact time when chatter is fully developed. That IF provides the needed reso- lution for identifying the onset of chatter suggests that the stability of the process should be monitored in the time-frequency domain to effectively detect and characterize machining instability. It is deter- mined that for the cutting tests performed chatter of the workpiece and tool are associated with the changing of the spectral components and more specifically period-doubling bifurcation.

Dynamics of Turning Operation Part II: Model Validation and Stability at High Speed

pp. 35-52 | DOI: 10.5890/JVTSD.2017.03.003

Eric B. Halfmann, C. Steve Suh, Wayne N.P. Hung

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Abstract

A comprehensive three-dimensional turning model is validated by comparing numerical simulations to the experimental data obtained in Part 1 using instantaneous frequency. Comparison of chatter-free cutting demonstrates that the model effectively captures the work- piece natural frequency, tool natural frequency, a nonlinear mode, and the spindle speed, which are main components of the underlying dynamics observed experimentally. The model accurately simulates chatter vibrations characterized as increased vibration amplitude and the appearance of coupled tool õworkpiece vibrations at a chatter frequency. The stability diagram constructed by running the model at various spindle speeds and depth-of-cuts demonstrates a general increase in the chatter-free critical depth-of-cut as the spindle speed increased. This chatter-free limit levels out as the spindle speeds exceeded 1500 rpm. At high spindle speeds the workpiece motions dominate the cutting dynamics, resulting in cases of excessive work- piece vibration amplitude and highly nonlinear frequencies which af- fect the efficiency of the process. The excessive workpiece amplitude cases create a second stability limit to be considered as a result of imbalance and configuration of the workpiece. Thus, workpiece dy- namics should not be neglected in mathematical and experimental analyses for the design of machine tools and robust cutting control law.

Model Reduction for Second Order in Time Nonlinear Dissipative Autonomous Dynamic Systems

pp. 53-63 | DOI: 10.5890/JVTSD.2017.03.004

Yan Liu, Jiazhong Zhang, Jiahui Chen, Yamiao Zhang

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Abstract

In light of Approximate Inertial Manifolds stemmed from nonlinear dynamics and Mode Analysis Technique in linear structural dynam- ics, a combined method is presented to reduce the second order in time nonlinear dissipative autonomous dynamic systems with higher dimension or many degrees-of-freedom to lower dimensional systems, and the ensuing error estimate is investigated theoretically. By this method, the system is studied in the phase space with a distance definition which can describe the distance between the original and reduced systems, and the solution of the original system is then pro- jected onto the complete space spanned by the eigenvectors of the linear operator of the governing equations. With the introduction of an Approximate Inertial Manifolds, the interaction between lower and higher modes or the influence of higher modes on the long-term behaviors, which will be ignored if the traditional Galerkin proce- dure is used to approach the governing equation, is considered to improve the distance between the original and reduced systems. Ad- ditionally, the error estimate for the approximation to the attractor is presented, and an explicit iterative scheme is then proposed to ap- proach the Approximate Inertial Manifolds. Finally, a comparison between the traditional Galerkin method and the method presented has been given and discussed. The results show that the method presented can provide a better and acceptable approximation to the long-term behaviors of the second order in time nonlinear dissipative autonomous dynamic systems with many degrees-of-freedom, espe- cially for the numerical analysis of complex bifurcation and chaos in complicated dynamical systems.

Redundant Control of A Bipedal Robot Moving from Sitting to Standing

pp. 65-71 | DOI: 10.5890/JVTSD.2017.03.005

Jing Lu, Xian-Guo Tuo, Yong Liu, Tong Shen

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Abstract

To control a multi-joints bipedal robot, it is necessary to choose a proper law of control that ensures the safe and stable motions of the robot. Even for the simplest postures, such as sitting and stand- ing, there are constraints to respect so that the inverse geometric model (MGI) would not have innitive solutions. In this paper, a particular task of sitting-to-standing is simulated for a bipedal robot using MATLAB. The articulation evolution and the variation of the shoulder position are evaluated using typical control and hierarchical redundant control in which the cases of with and without constraints are both considered. The simulation results show that the hierarchi- cal redundant control has a better effect than the typical one, and when considering the constraints, the articulations' angular velocities vary more smoothly so that the motor is better protected.

Time-delay Effects on Periodic Motions in a Periodically Forced, Time-Delayed, Hardening Duffing Oscillator

pp. 73-91 | DOI: 10.5890/JVTSD.2017.03.006

Albert C.J. Luo†, Siyuan Xing

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Abstract

In this paper, time-delay effects on periodic motions in a periodi- cally forced, time-delayed, hardening Duffing oscillator are discussed. One often considers the time-delay interval is very small compared to the oscillation period. In engineering application, the time-delay interval is often very large. Bifurcation trees of periodic motions to chaos varying with time-delay are presented for such a time-delayed, Duffing oscillator. Using the nite discrete Fourier series, harmonic amplitude varying with time-delay for stable and unstable solutions of period-1 to period-4 motions are developed. From the analytical prediction, numerical results of periodic motions in the time-delayed, hardening Duffing oscillator are completed. Through the numerical illustrations, time-delay effects on period-1 motions to chaos in non- linear dynamical systems are strongly dependent on the distributions and quantity levels of harmonic amplitudes.

JVTSD Volume 1, Issue 2

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Complete Bifurcation Trees of a Parametrically Driven Pendulum

pp. 93-134 | DOI: 10.5890/JVTSD.2017.06.001

Yu Guo1 , Albert C.J. Luo2†

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Abstract

In this paper, the complete bifurcation trees of a parametrically driven pendulum are investigated using discrete implicit maps obtained through a mid-point scheme. Based on the discrete maps, mapping structures are developed for periodic motions in such a parametric system. Analytical bifurcation trees of periodic motions to chaos are developed through the nonlinear algebraic equations of such implicit maps. The stability and bifurcation of periodic motions is carried out through eigenvalue analysis. For a better understanding of the motion complexity in such a system, the corresponding frequency-amplitude characteristics are presented. Finally, numerical results of periodic motions are illustrated in verification. Many new periodic motions in the parametrically excited pendulum are discovered.

Three-component Parallel and Synchronous Seismic Data Acquisition Based on Time-division Sampling System

pp. 135-141 | DOI: 10.5890/JVTSD.2017.06.002

Tong Shen, Xian-Guo Tuo, Yong Liu, Jing Lu

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Abstract

To economize power dissipation and volume of the three-component parallel and synchronous seismic data acquisition system, under the inspiration of sampling rate conversion theory in the digital signal processing, a project of three-component parallel and synchronous seismic data acquisition method is proposed based on time-division sampling system, in which triple interpolation is implemented in the three sets of data acquired by time-division sampling. Then another interpolation or decimation is carried out to aim at converting sampling rate of the system into the target value. Results of the error analysis show that the accuracy of numerical calculation in this conversion process is superior to the resolution ratio of hardware system. the prominent dominant of this project is that power dissipation and volume of parallel and synchronous acquisition system applied to band-limited signal are optimized and performance of the whole system is improved.

Experimental Research on Surge Characteristics of Centrifugal Compressors

pp. 143-152 | DOI: 10.5890/JVTSD.2017.06.003

Zhao Yuanyang†, Yang Qichao , Li Liansheng , Liu Guangbin , Shu Yue

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Abstract

Centrifugal compressors are widely used in many process industries. The stability is one of the most important characteristics of centrifugal compressor. When the compressor operates under the condition of small mass flow rate, the working conditions of rotating stall and surge will occur. The surge of the centrifugal compressor is researched by experiment. The signals are tested and analyzed when surge condition occurs in this paper. The suction and discharge pressures are tested under the surge working conditions. The pulsation frequency of the pressures is very small (6Hz), and it is about 0.03 of the rotating speed frequency. The vibration of the inlet pipes is researched as a parameter of the surge of compressor. The vibration test results show that it can be as an important signal to estimate the surge working condition. When the surge occurs, the pipe vibration amplitude at the low frequency is bigger, and it is about four times of that at the working frequency. However, the maximum amplitude of pipe vibration is not change with rotation speeds.

Advances in Modal Analysis Application

pp. 153-166 | DOI: 10.5890/JVTSD.2017.06.004

Ahmed El-Khatib , M.G.A. Nassef†

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Abstract

Realization of modal analysis in a wide spectrum of applications has been established since decades. The dynamic characteristics obtained from analytical and experimental modal analysis helped researchers as well as engineers to determine the dynamic behavior of structures and assemblies. Extensive research work is given to the detection and evaluation of damages in mechanical structures using knowledge of modal frequencies and mode shapes. The fact that the dynamic characteristics thus obtained, are influenced by the structure’s physical and mechanical properties has inspired many researchers, recently to use modal analysis as a tool for the identification of mechanical properties and remaining life prediction of manufactured components. It is not the intention of the authors in this paper to investigate the knowhow of each of the applications mentioned within the scope of the paper; since the reader can obtain detailed information of most of the applications from the respective references written at the end of this paper. The main objective of this paper, is to summarize different important applications of modal analysis and classify these applications into three main categories; quality assessment, material characterization, and life prediction. The work also describes what has been studied in each category and provides an insight for researchers on what still needs to be achieved. Accordingly; the authors introduce a new application that will revolutionize the basis on which engineering design is traditionally used, by the fact that it is better testing the product instead of testing the material from which the product will be made. This new philosophy is currently worked upon by the authors.

Design and Dynamic Analysis of Bending Waves Waveguide Based on Coordinate Transformation Theory

pp. 167-175 | DOI: 10.5890/JVTSD.2017.06.005

Xing Chen , Li Cai , Ji-HongWen †

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Abstract

The finite embedded coordinate transformation theory is introduced into the elastic dynamic equation of bending waves, a design of bend waveguide to control bending waves to bend at arbitrary angel is proposed. The formula to describe the transformed materials properties in an elastic thin plate is obtained, which contains anisotropic heterogeneous Young modulus and a radially dependent mass density. Through homogenization of layered periodic composite materials, the anisotropic materials are dispersed into discrete layered isotropic materials. The simulation model of the waveguide is built, and full-wave dynamic simulations of the model are analyst with finite element method. Numerical analysis results show that the waveguide consisting of 10 layers alternating two types of isotropic elastic materials can achieve effective control of the bending wave propagation in thin plates, it works over the frequency range [1500, 10000] hertz with ultra-wideband characteristics. The study can provide technological approaches to bending waves control in thin plates, and it is expected to provide potential applications in isolating structures from vibrations.

JVTSD Volume 1, Issue 3

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On The Temporal and Spectral Characteristics of Micro-Milling Dynamics

pp. 177-193 | DOI: 10.5890/JVTSD.2017.09.001

Eric B. Halfmann, C. Steve Suh†

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Abstract

Due to different chip formation mechanisms, increased tool-radius to feed-rate ratio, and higher spindle speeds, micro-milling is a highly nonlinear process which can produce multiple and broadband frequencies that negatively impact the process. Micro-milling is investigated through the development and analysis of a nonlinear micromilling dynamic model. A lumped mass-spring-damper system is assumed for modeling the dynamic properties of the tool. The force mechanism utilized is a slip-line field model that provides the advantage of being highly dynamic by accounting for the constantly changing effective rake angle and slip-line variables. Accurate prediction of the chip thickness is important in correctly predicting the dynamics of the system since the force mechanism and its variables are a function of the chip thickness. A novel approach for calculating the instantaneous chip thickness which accounts for the tool jumping out of the cut and elastic recovery of the workpiece is presented. The derivation for the effective rake angle is given and the helical angle is accounted for resulting in a three dimensional micro-milling model. The model generates the high frequency force components that are seen in experimental data available in literature. The effect that the helical angle and system stiffness has on the resulting cutting forces is also investigated. It is shown that dynamic instability has the greatest impact on tool performance and improving the dynamic response is a necessity for achieving high speed ultra-stable micro-machining.

Evaluation of 3D Measurement Performance of Laser Scanner with Simplified Receiver Optics

pp. 195-206 | DOI: 10.5890/JVTSD.2017.09.002

Kohei Kawazoe1, Takahiro Kubota1, Yoshihiro Deguchi2†

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Abstract

Development of autonomous drive or control technology for vehicles such as a car or a railway train has become major trends, so there is great need for a 3D measuring system which detects terrains or obstructs on forward area of the vehicle. The authors developed a simplified receiver optical system for the line scan type laser scanner which is one of the 3D measurement methods using laser ranging and mirror scanning. The developed receiver enables to acquire the 3D data with wider FOV (field of view) without a receiver scanner mirror. The receiver optics can spatially resolve the measured area horizontally and can measure the whole vertical FOV without scanning. The composition of the receiver optical system was obtained by an optical simulation. After an evaluation system was constructed combining a laser transmitter, a processing unit and the developed receiver, the performance tests were carried out under indoor and outdoor conditions. In this paper, the main objective is an evaluation of the FOV enlargement function of the developed receiver in vertical direction. And it also describes about the 3D measurement performance of the system using the receiver. The results of tests showed that the vertical FOV was extended 6.6 times with the receiver than a conventional one as designed. And it was verified that the system had 3D measurement capability with target distance error of -0.10 ∼ +0.18m in outdoor test.

A Generalized Lattice Boltzmann Model for Simulating Axisymmetric Convective Flow in Porous Media

pp. 207-217 | DOI: 10.5890/JVTSD.2017.09.003

Zuo Wang , Jiazhong Zhang†, Nannan Dang , Biwu Huang

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Abstract

Axisymmetric convective flow in porous media is frequently encountered in nature and industry applications. In recent years, Lattice Boltzmann method has been developed as a powerful tool for such kind of flow and heat transfer. Despite its success in many problems regarding to porous flow, the existing LB model for the axisymmetric thermal flow in porous media at the representative volume scale suffers from a serious drawback. That is, it can not handle the cases where the heat capacitance of porous media varies spatially obviously. In this paper, a generalized LB model for axisymmetric temperature field is proposed to remedy this shortcoming. Chapman-Enskog analysis demonstrates that the energy equation in the cylindrical coordinates system can be recovered by the proposed model. Natural convection in a vertical annulus filled with saturated porous media, natural convection in a vertical annulus without porous media, have been carried out, and the results predicted by the present LB model agree well with the existing numerical data. More, natural convection in a vertical annulus with spatially varying heat capacitance shows that the present model can address the problem where the heat capacitance varies spatially obviously successfully.

Steering Control for a Class of Nonholonomic Wheeled Mobile Robots Using Adaptive Back Stepping

pp. 219-245 | DOI: 10.5890/JVTSD.2017.09.004

Abdul Baseer Satti†, Faisal Nadeem

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Abstract

This paper presents a simple method of steering control strategy for a class of Nonholonomic wheeled mobile robots. The strategy is based on adaptive Backstepping technique and does not require the conversion of the model into a “chained form”, and so it does not depend on any special transformation methods. Control laws have been developed for five different types of mobile robot models. The control laws and the adaptive laws are derived in the sense of Lyapunov functions, so that the closed loop system’s stability can be guaranteed.

Steering Control of an Underwater Vehicle using Adaptive Back Stepping Approach

pp. 247-265 | DOI: 10.5890/JVTSD.2017.09.005

Abdul Baseer Satti†, Faisal Nadeem

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Abstract

This paper presents a simple and systematic approach to steer an underwater vehicle model by considering two different cases: (i) when all actuators are functional, and (ii) when one actuator is not working. In first case, the model of an underwater vehicle is steered by using adaptive Backstepping technique. The first actuator is necessary for the operation of the system so any of the other three actuators can be non-operational. So, the second case itself contains three different cases. Adaptive Backstepping is then used to steer the system with one non-working actuator. The synthesis method is general, in that it applies to a large class of drift free, completely controllable systems, for which the associated controllability Lie algebra is locally nilpotent.

Mathematical Framework and Non-Linear Modeling of the Mechanical System. Part I: Rigid Body Kinematics

pp. 267-280 | DOI: 10.5890/JVTSD.2017.09.006

S. Haddout†, M. Rhazi , S.E. Faik , A. Soukri

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Abstract

In the present paper, a problem of a free rigid body motion in mechanical system is analyzed from a video capture webcam (Sony Cybershot 10.1 M.P). The problem subjected to kinematic characteristics and relative trajectories are theoretically and analytically solved. Subsequently, the solution is quantitatively verified by a new experiment procedure, constructed by the authors. The geometrical treatments of the absolute experimental trajectories of two points of the body, allow determining the relative trajectory of a point from the other point. The kinematic parameters optimization, i.e., translational velocity, instantaneous velocity of rotation and initial kinematic conditions, are obtained, solving non-linear least-squares problems, based on Levenberg-Marquardt’s algorithm. On the other hand, the response surfaces of the objective function and the sensitivity analysis of the different initial estimates of the analytical model parameters are also discussed. The comparison of the theoretical study results with experimental output shows that there are instruments to directly verify rather abstract mathematical theories even on the general mechanics program. Moreover, combining the theoretical description of the problem with an appropriate laboratory experiment and computational optimization procedures, gives a more exhaustive view of the physical problem as a whole.

JVTSD Volume 1, Issue 4

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A Time-Frequency PID Controller Design for Improved Anti-Interference Performance of a Solenoid Valve Applicable to Hydraulic Cylinder Actuation

pp. 281-294 | DOI: 10.5890/JVTSD.2017.12.001

Xiu-Heng Wu1, Zheng-He Song1†, Yue-Feng Du1, En-Rong Mao1, C. Steve Suh2

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Abstract

PID control is widely used in electro-hydraulic systems. However, enhancing PID control performance in response to system nonlinearity, fluctuations of external load, and noise inevitably renders the chattering of the system that are also telltale indications of poor efficiency and dynamic instability. On the other hand, tuning down PID parameters would alleviate chatter at the expenses of reduced performance and inefficient use of resources. To address the particular issue, a novel controller concept termed as the time-frequency PID (TFPID) is developed. Firstly, a nonlinear electro-hydraulic dynamic model to be controlled is built for numerical and physical studies. Next, the working principle of the TFPID control is elaborated where the discrete wavelet transform is employed to decompose the error signal into high frequency error and low frequency error. Two unique PID controllers incorporating proportion, differential, and integral control are designed to mitigate the two error signals. The TFPID controller and system model are developed in MATLAB/Simulink to optimize the parameters and a hardware-in-the-loop test bench is employed to establish the performance of the system subject to interferences. Physical test results show that TFPID performs significantly better in anti-interference, stability, and dynamic response.

Impact of Tool Geometry and Tool Feed on Machining Stability

pp. 295-317 | DOI: 10.5890/JVTSD.2017.12.002

Achala V. Dassanayake, C. Steve Suh†

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Abstract

Tool-workpiece dynamics is characterized by aperiodic responses in- cluding period-doubling bifurcation and chaos. As a state signifying the extent of machining instability, tool chatter in longitudinal turn- ing operation is a function of nonlinear regenerative cutting force, instantaneous depth-of-cut (DOC), and workpiece whirling. The ef- fects of tool geometry and feed rate per revolution on cutting stability are investigated using a comprehensive model previously reported in References [1–3]. The model configuration allows the coupled tool- workpiece motion relative to the machining surface to be studied in the Cartesian space as a function of spindle speed, instantaneous DOC, rate of material removal, tool geometry, and material imbal- ance induced whirling. It is found that chatter can be eminent using one set of tool geometry while, at the same DOC, be sufficiently sup- pressed by employing tool inserts of different geometric parameters. Nonlinearity of tool structure is shown to have a dominant effect on tool vibration amplitude. High feed rate contributes to stability at high DOCs, thus indicating that feed rate is among the parameters that impact cutting stability.

The Ackerman Steered Car Non-Holonomic Lagrangian Mechanics System: Mathematics Problem Treatment of the Geometrical Theory

pp. 319-331 | DOI: 10.5890/JVTSD.2017.12.003

Soufiane Haddout1†, Zhiyi Chen2, Mohamed Ait Guennoun1

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Abstract

Mechanical systems have traditionally provided a fertile area of study for researchers interested in nonlinear control, due to the inherent nonlinearities and the Lagrangian structure of these systems. Recently, a great deal of emphasis has been placed on studying systems with nonholonomic constraints, including mobile wheeled robots and multiple-trailer vehicles, where the wheels provide a no-slip velocity constraint. In this paper, a new methods in non-holonomic mechanics are applied to a problem of an ackerman steered car motion for the first time. This method of the geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces, was proposed and developed in the last decade by Krupkov´a in 1990’s. The relevance of this theory for general types of nonholonomic constraints, not only linear or affine ones, was then verified on appropriate models. Frequently considered constraints on real physical systems are based on rolling without sliding, i.e. they are holonomic, or semi-holonomic, i.e. integrable. Moreover, there exist some practical examples of systems subjected to true (non-integrable) nonholonomic constraint conditions. On the other hand, the equations of motion of an ackerman steered car are highly nonlinear and rolling without slipping condition can only be expressed by nonholonomic constraint equations. In this paper, the geometrical theory is applied to the above mentioned mechanical problem using the above mentioned Krupkov´a approach. The results of numerical solutions of constrained equations of motion, derived within the theory, are presented and thus they open the possibility of direct application of the theory to practical situations in engineers.

Flow-induced Vibration of Flexible Bottom Wall in a Lid-driven Cavity

pp. 333-341 | DOI: 10.5890/JVTSD.2017.12.004

Xu Sun†, Wenxin Li, Zehua Ye

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Abstract

Flow-induced vibration of the flexible bottom wall in a lid-driven cavity is investigated numerically using a well-validated finite element scheme for fluid-structure interaction (FSI). First, the mechanical and mathematical models of a lid-driven cavity with flexible bottom are presented, and the corresponding FSI solution procedure is introduced briefly. Then, the accuracy and stability of the developed FSI scheme and code are examined and a grid independence test is carried out. Finally, using very fine increment, bifurcations of the flow-induced vibration (FIV) of the flexible bottom with respect to the structure rigidity and Reynolds number are studied in detail. The results could reveal more details of the benchmark FSI model involving a lid-driven cavity with flexible bottom, gaining a better understanding on other FIVs caused by the internal unsteady flows.

Fast Unbalancing of Rotating Machines by Combination of Computer Vision and Vibration Data Analysis

pp. 343-352 | DOI: 10.5890/JVTSD.2017.12.005

A. Najedpak, C. Yang†

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Abstract

Unbalance is one of the most common mechanical faults in rotating machines. Although different balancing methods have been developed, most of them require balancing machine to perform unbalance correction. A method using accelerometers data and intricate vibration theories can eliminate the need of balancing machine, and the amplitude and phase of the machine’s vibrations can be identified. However it needs numerous measurements, and in some cases it is even impossible to be implemented. To overcome this problem, a novel approach with reduced number of measurements is presented in this paper. The proposed method requires only two measurements: one from original unbalanced condition, and the other from modified situation after adding an arbitrary trial mass to a marked location. The rotating rotor is being video recorded under original unbalanced and modified situations. The position of the marked area is identified when the amplitude of the sinusoidal vibration response reaches the maximum. The correction mass and its adding location are calculated using proposed method. To demonstrate the effectiveness of our method, an experiment is setup. Vibrations under healthy, unbalanced and balanced conditions are analyzed. The results demonstrated that the developed method is more cost effective with the same accuracy as the other contested balancing techniques.

Towards Infinite Bifurcation Trees of Period-1 Motions to Chaos in a Time-delayed, Twin-well Duffing Oscillator

pp. 353-392 | DOI: 10.5890/JVTSD.2017.12.006

Siyuan Xing, Albert C.J. Luo†

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Abstract

In this paper, bifurcation trees of periodic motions to chaos in a periodically forced, time-delayed, twin-well Duffing oscillator are pre- dicted by a semi-analytical method. The twin-well Duffing oscilla tor is extensively used in physics and engineering. The bifurcation trees of periodic motions to chaos in nonlinear dynamical systems is very significant for determine motion complexity. Thus, the bi furcation trees for periodic motions to chaos in such a time-delayed, twin-well Duffing oscillator are obtained analytically. From the fi nite discrete Fourier series, harmonic frequency-amplitude character istics for period-1 to period-4 motions are analyzed. The stability and bifurcation behaviors of the time-delayed Duffing oscillator are different from the non-time-delayed Duffing oscillator. From the an alytical prediction, numerical illustrations of periodic motions in the time-delayed, twin-well Duffing oscillator are completed. The com plexity of period-1 motions to chaos in nonlinear dynamical systems are strongly dependent on the distributions and quantity levels of harmonic amplitudes. As a slowly varying excitation becomes very slow, the excitation amplitude will approach infinity for the infinite bifurcation trees of period-1 motion to chaos. Thus infinite bifurca tion trees of period-1 motion to chaos can be obtained.

JVTSD Volume 2, Issue 1

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Electromagnetic Control of Nonlinear Behavior of an Excited Cantilever Beam in a Single Mode Approximation

pp. 1-8 | DOI: 10.5890/JVTSD.2018.03.001

Amine Bichri, Jarir Mahfoud, Mohamed Belhaq

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Abstract

The eﬀects of combined DC and fast AC electromagnetic actuations on the dynamic behavior of an excited cantilever beam is studied considering a single mode approximation. Analytical investigation is performed to extract the equation of motion describing the slow dynamic of the system. The inﬂuence of the fast AC actuation and the air gap on the nonlinear behavior of the system is examined. It is shown that the nonlinear characteristic of the system can be controlled by appropriately tuning the AC actuation or the air gap. This can be useful in certain engineering applications where the operating frequency range includes one or several critical frequencies that should be avoided.

Theory and Analysis of Impulsive Type Pantograph Equations with Katugampola Fractional Derivative

pp. 9-20 | DOI: 10.5890/JVTSD.2018.03.002

D. Vivek, K. Kanagarajan, S. Harikrishnan

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Abstract

In this paper, we investigate the existence, uniqueness and Ulam stability of solutions for impulsive type pantograph equations with Katugampola fractional derivative. The arguments are based upon the Banach contraction principle and Schaefer’s ﬁxed point theorem.

Non-horizontally Suspended Cable Dynamics with Flexible Tower Modulations: Free and Forced Vibrations

pp. 21-32 | DOI: 10.5890/JVTSD.2018.03.003

Tie-Ding Guo, Lian-Hua Wang, Hou-Jun Kang, Yue-Yu Zhao

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Abstract

Based upon an asymptotically reduced coupled model, nonlinear forced vibrations of a non-horizontally suspended cable is investigated in this paper, which is coupled with a ﬂexible oscillating tower. The cable’s nonlinear coupled dynamics is a modulated version of cable’s uncoupled dynamics, i.e., the cable dynamics with ﬁxed rigid towers. Nonlinear frequency responses of the cable-tower coupled system are found, with saddle-node bifurcations, Hopf bifurcations, and quasi-periodic behaviors detected. Special attentions are paid to the dynamic eﬀects caused by cable-tower coupling, boundary damping, and the inclinations.

Analysis of nonlinear neutral pantograph differential equations with y-fractional derivative

pp. 33-41 | DOI: 10.5890/JVTSD.2018.03.004

S. Harikrishnan, K. Kanagarajan, D. Vivek

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Abstract

In this paper, we discuss the existence, uniqueness and stability of nonlinear neutral pantograph equation with ψ -fractional derivative. The arguments are based upon Schauder ﬁxed point theorem and Banach contraction principle. Moreover, we discuss the Ulam-Hyers type stability.

A Discrete Fourier Transform Based Dithering Signal Generation Method for Reduced Quantization Error

pp. 43-51 | DOI: 10.5890/JVTSD.2018.03.005

Chang-Qing Ye, Xing-Zhong Xiong

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Abstract

Addressing the impact of quantization error in analog-to-digital converter (ADC) for signal processing, a Discrete Fourier Transform (DFT) based method for the generation of dithering signals is presented. Eﬀective in reducing quantization error, the dithering signal generated using the method is not only independent of the input signal but also can improve the performance of the ADC. To illustrate the advantages of the dithering signal reconstructed using the method, three kinds of typical dithering eﬀects, namely, Triangular Distribution Dithering, Gaussian Distribution Dithering and Uniform Distribution Dithering on the quantization error in an ADC are considered. The properties of three practical dithering signals are investigated. It is shown that while these typical dithering may be useful they are some potential problems. The dithering signals reconstructed using the DFT based generation scheme is shown to contribute signiﬁcantly to reducing quantization error. Numerical experiments and theoretical analyses demonstrate that the DFT based dithering reconstruction can obtain prominent performance for ADC in comparison to typical dithering signals.

A Similitude Design Method of Rotating Thin-wall Short Cylindrical Shell Considering Nonlinear Vibration Response

pp. 53-67 | DOI: 10.5890/JVTSD.2018.03.006

Zhong Luo, Yunpeng Zhu, You Wang, Fei Wang, Qingkai Han

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Abstract

This study investigates the non-linear dynamic scaling laws for a rotating thin-wall short cylindrical shell. By introducing the geometric non-linear term, corresponding governing equations are employed to establish the non-linear scaling laws. Both the natural frequency and single-point excitation response of the rotating cylindrical shell are investigated. The applicability of the scaling laws of the rotating thin-wall short cylindrical shell is veriﬁed numerically. In addition, the scaling laws for linear and non-linear vibrations are compared. Analytical results indicate that the scaled model designed by the non-linear scaling laws are more restrictive than that of using the linear scaling laws. In addition, they predict the characteristics of the prototype with good accuracy.

An Active Vibration Suppression of Rotor Unbalance through an Adaptive Control Method Based on Self-adjusting of PD Gain

pp. 69-81 | DOI: 10.5890/JVTSD.2018.03.007

Jian-Fei Yao, Jia-Bao Dai, Liang Liu, Feng-yu Yang, Shu-cheng Gao

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Abstract

The attention is conﬁned to the vibration suppression of rotor unbalance in this paper. A method to control synchronous vibration due to rotor unbalance in rotor-bearings system is proposed which uses active magnetic actuator (AMA) to produce active control force to suppress rotor’s vibration. A model reference adaptive control strategy based on self-adjusting of Proportional and Diﬀerential gain is adopt for producing active electromagnetic force. First the model of rotor-bearing system with AMA and the ideal reference model are established using the ﬁnite element and the state space method. Then on the basis of PD feedback, the adaptive control of feedforward and unbalance compensation is considered. An active vibration control scheme for controlling transverse vibration of rotor due to unbalance excitation is designed. Finally, numerical example and simulated analysis for controlling synchronous vibration of rotor are carried out. The simulation results indicate that the proposed approach can eﬀectively suppress the synchronous vibration caused by rotor unbalance using the electromagnetic force.

Study on Flow-Induced Excitation Force on the Last Stage Blade of Steam Turbine

pp. 83-90 | 10.5890/JVTSD.2018.03.008

Sheng Ren†, Hua-Yun Zhu, Xu-Dong Ding, Zhi-Ming Xu, Yong-Feng Sui

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Abstract

Combining transient blade row (TBR) method with stationary inverse Fourier transformation (IFT), an eﬀective method for numerical simulation of ﬂow-induced force on the blade at the last stage of steam turbine is proposed in this study. Using this method, only a single ﬂow channel needs simulating transiently to obtain the force on blade. Then, the numerical simulation of ﬂow-induced force using this method is carried out on the last stage of a real steam turbine, and the feasibility of this method is also veriﬁed via this example. Comparing with traditional transient computation, a remarkable amount of computing time and resources can be saved by this method.

JVTSD Volume 2, Issue 2

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A Fuzzy Logic PI Trajectory Following Control in a Chaotically Loaded Real Mechatronic Dynamical System with Stick-Slip Friction

pp. 91-107 | DOI: 10.5890/JVTSD.2018.06.001

Wojciech Kunikowski, Paweł Olejnik, Jan Awrejcewicz

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Abstract

Fuzzy logic control algorithms are regarded to as a relatively new concept in modern control theory. This paper presents a comparative analysis of two qualitatively diﬀerent approaches used for angular velocity control of a DC motor subject to chaotic disturbances coming from a gear with a transmission belt carrying a vibrating load. The purpose is to achieve accurate control of speed of the DC motor (a plant), especially, when the motor parameters and some external loading conditions are partially unknown. First, the classical approach based on the PID control is considered, and then a fuzzy logic based alternative is proposed. Two diﬀerent controllers are developed, i.e. the classical PID controller and a Mamdani type fuzzy logic PI controller. Both control algorithms are implemented on an 8-bit AVR ATmega644PA microcontroller. Based on step responses of the plant, an analysis as well as an interesting comparison of the controllers’ performance has been presented.

Extreming curves and the parameter space of a generalized Logistic mapping

pp. 109-118 | DOI: 10.5890/JVTSD.2018.06.002

Diogo Ricardo da Costa, Matheus Hansen, Edson D. Leonel, Rene O. Medrano-T

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Abstract

A logistic map with parametric perturbation is studied. We conﬁrm the model exhibits self-similar structures in the parameter space known as shrimps. The organization of such structures may be describe through extreme curves, giving exactly the position of each one of them in a complicated behavior in the parameter space. Boundary crisis are also discussed. They lead to an abrupt destruction of the chaotic attractor and how such destruction aﬀects the dynamics of the system is discussed, particularly aﬀecting the time before the orbit leaves to inﬁnite. By a speciﬁc choice of the parameters we show the existence of strange non-chaotic attractors in the parameter space.

A Series of Symmetric Period-1 Motions to Chaos in a Two-degree-of-freedom van der Pol-Duffing Oscillator

pp. 119-153 | DOI: 10.5890/JVTSD.2018.06.003

Yeyin Xu, Albert C.J. Luo

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Abstract

In this paper, independent periodic motions in the two-degree-offreedom (2-DOF) van der Pol-Duﬃng oscillator are investigated. From the semi-analytical method, the 2-DOF van der Pol-Duﬃng oscillator is discretized to obtain implicit discrete mappings. From the implicit mapping structures, periodic motions varying with excitation frequency are obtained semi-analytically, and the corresponding stability and bifurcation are obtained by eigenvalue analysis. The frequency-amplitude characteristics of periodic motions are also presented. Thus, from the analytical prediction, numerical simulations of periodic motions are performed for comparison of numerical and analytical results. The harmonic amplitude spectrums of periodic motions are also presented for harmonic eﬀects on the periodic motions. Through this study, the order of symmetric period-1 to chaotic motions (i.e., 1(S)⊳1(A)⊳3(S)⊳2(A)⊳···⊳m(A)⊳(2m+1)(S)⊳···) (m→∞) is discovered. Chaotic motions or catastrophe jumping phenomena between the two independent periodic motions exist. The independent periodic motions can be used for speciﬁc applications in phase locking, and such results can be useful to develop series of the van der Pol-Duﬃng circuits for applications.

Lift Enhancement of Airfoil Using Local Flexible Structure and the Influences of Structure Parameters

pp. 155-165 | DOI: 10.5890/JVTSD.2018.06.004

Pengfei Lei, Jiazhong Zhang, Daxiong Liao

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Abstract

The local ﬂexible structure (LFS) is used on the airfoil to enhance the lift, and the inﬂuences of structure parameters of LFS on the lift enhancement are studied numerically. Coupling with the structure solver, the unsteady ﬂows over airfoil with LFS are simulated by using the CBS-ALE scheme and dual time stepping. The results show that the amplitude oscillation is the key factor to enhance the lift as the self-induced oscillation is used. The large oscillation amplitude of LFS can only be induced in certain frequency range with suitable structure parameters, such as smaller elastic stiﬀness and damping. The oscillation of LFS can lead to the formation of individual separation bubble and vortex, which are beneﬁcial to the lift enhancement of airfoil. With large oscillation amplitude, vortices with low pressure can be generated early and stay on upper surface of airfoil for a long time, resulting in the signiﬁcant lift enhancement.

Continuous Stabilizing Control for a Class Of Non-holonomic systems: Brockett System Example

pp. 167-172 | DOI: 10.5890/JVTSD.2018.06.005

Fazal Ur Rehman, A. Baseer Satti, A.Ahmed Saleem

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Abstract

A continuous adaptive controller is designed for a famous example of Brockett system which is an example of a class of non-holonomic systems. The controllability Lie Algebra of the Brockett’s system contains Lie brackets of depth one. It is shown that the closed loop system is globally uniformly asymptotically stable. The advantage of this method is that it does not require the conversion of the system model into a “chained form,” and thus does not rely on any special transformation techniques. The practical eﬀectiveness of the controller is illustrated by numerical simulations.

Remaining useful lifetime prediction of gas turbine bearings based on experiment vibration signals data

pp. 173-185 | DOI: 10.5890/JVTSD.2018.06.006

Boulanouar Saadat, Ahmed Hafaifa, Ali Bennani, Nadji Hadroug, Abdellah Kouzou, Mohamed Haddar

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Abstract

Gas turbines are widely found in industries, especially in gas compressor stations, where they are used to ensure the transportation of gas in high pressure pipelines over a long distance. Nevertheless, these rotating machines are subject to vibrations due to the inﬂuence of several causes, such as mass imbalance and shaft misalignment. These vibrations can aﬀect directly the bearings, where their lifespan can be shorten remarkably. Furthermore they can be damaged causing catastrophic failure in the gas turbine and its installation. The main purpose of this paper is to develop an approach that can provide the estimated remaining life of the gas turbine bearings based on the vibration signals obtained via installed sensors. This approach allows us to estimate the optimal expected life of the studied gas turbine bearings by the prediction of the expected failures times. The obtained result under the proposed approachis satisfactory and shows that the use of the proposed approach can avoid the costly damage caused by the mentioned failures in the gas turbine under the imposed constraints.

JVTSD Volume 2, Issue 3

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A Modified Newmark Scheme for Simulating Dynamical Behavior of MDOF Nonlinear Systems

pp. 187-207 | DOI: 10.5890/JVTSD.2018.09.001

S.D. Yu, M. Fadaee

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Abstract

The Newmark integration scheme, originally developed for simulating responses of linear dynamical systems, is modiﬁed in this paper to eﬀectively model nonlinearities through introduction of the incremental displacements and the eﬀective mass, damping and stiﬀness matrices. Based on the results of comparisons with the analytical solutions and the Runge-Kutta (RK) method for well-known nonlinear oscillators, the proposed scheme is found to capture accurately dynamical behaviors of nonlinear systems such as amplitude-dependent stiﬀening or softening natural frequencies, jump phenomena, superharmonic resonances, sub-harmonic resonances, and even chaos and bifurcations. The proposed scheme is more eﬃcient than the RK method for large scale nonlinear systems with some type of sparsity for which a targeted algebraic equations solver can be employed to speed up the solution for each time step.

Experimental Investigations of Energy Recovery from an Electromagnetic Pendulum Vibration Absorber

pp. 209-219 | DOI: 10.5890/JVTSD.2018.09.002

Krzysztof Kecik, Angelika Zaszczynska, Andrzej Mitura

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Abstract

The paper presents an experimental study of a special non−linear low frequency system dedicated to vibration mitigation and energy recovery. The dual−function design was based on an autoparametric vibration system, which consists of an oscillator with an added pendulum vibration absorber. Its structure includes an energy harvesting device: a levitating magnet in a coil. The pendulum motion shows simultaneously the eﬀects of vibration reduction and energy recovery. The inﬂuences of the magnet−coil conﬁgurations, and load resistances on vibration reduction and energy harvesting were studied in detail.

Huge Size Structure Damage Localization and Severity Prediction: Numerical Mod-eling, Simulation and SVM Regression Method

pp. 221-237 | DOI: 10.5890/JVTSD.2018.09.003

Gang Jiang, Yiming Deng, Lili Liu, Canghai Liu, Zihong Liu, Yong Jiang

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Abstract

In systematic identiﬁcation for real bridge engineering structural damage evaluation, lack of “negative samples” is the main reason for misjudgment and false classiﬁcation. Aimed at this problem, the paper proposed a new kinetic-parameters-analysis-based method of damage identiﬁcation for bridge structures, using both numerical simulation and real experiments under controlled lab conditions. PROE and ADAMS were adopted to build structural models and integrate with simulation experiments under virtual force, frequency response data were gathered and used as “simulation datasets”. In real structural experiments, accelerators and advanced signal acquisition equipments were used to collect signals from real structures hit by real force. Signals gathered by equipments were used as “real datasets”, corresponded with “simulation datasets”. After that, features were extracted from these two kinds of datasets. Authors found that numerical simulation models were not always accurate, while real model had its own advantages and disadvantages. To ﬁll this gap, relationships between simulation and actual measurements were investigated in this paper. Finally, Support Vector Machine (SVM) method was used to perform pattern recognition experiments and showed its good performance on structure damage identiﬁcation. The proposed method is scalable and can be extended to a bigger structure, such as the entire bridge faults diagnosis.

A Low Cost Device for Excessive Vibration Detection in Electric Motors

pp. 239-247 | DOI: 10.5890/JVTSD.2018.09.004

M. Sundin, A. Babaei, S. Paudyal, C. Yang, N. Kaabouch

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Abstract

Health monitoring and fault diagnosis are essential to ensuring reliable operation of machinery in industry. In this paper, we present the design of a low cost device for sensing mechanical vibrations and detecting excessive vibration. Advantages of the device include cost eﬀectiveness and simplicity of the design. Piezoelectric-based sensor, light emitting diodes, resistors, and liquid crystal display, and an Arduino board are the main components of the device. The eﬀectiveness of designed device was tested on simple electric motors, such as fan and drill motors. This vibration measurement device can be used to monitor machinery health by detecting unwanted oscillations and subsequent potential hazards.

A new application of the normal form description to a N-dimensional dynamical systems attending the conditions of a Hopf bifurcation

pp. 249-256 | DOI: 10.5890/JVTSD.2018.09.005

Vinicius B. Silva, Joao P. Vieira and Edson D. Leonel

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Abstract

In this paper we prove the following theorem: consider a N-dimensional dynamical system that is reduced to its center manifold. If it is proved the system satisﬁes the conditions of a Hopf bifurcation theorem then the original system of diﬀerential equations describing the dynamics can be rewritten in a simpler analytical expression that preserves the phase space topology. The theorem proposed and proven eﬀectively reduces the work done to obtain the normal form for the class of dynamical systems with the occurrence of Hopf bifurcation.

Nonlinear Dynamics of a Reduced Cracked Rotor

pp. 257-269 | DOI: 10.5890/JVTSD.2018.09.006

K. Lu, Y. Lu, B. C. Zhou, W. Jian, Y. F. Yang, Y. L. Jin, Y. S. Chen

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Abstract

The transient proper orthogonal decomposition (TPOD) method is applied for order reduction in the rotor system in this paper. A 26DOFs rotor model with crack is established by the Newton’s second law, and the dynamical behaviors (bifurcation diagram, amplitude frequency curve, etc.) of the crack fault are discussed. The optimal reduced model can be provided by the proper orthogonal mode (POM) energy method, the TPOD method is applied to reduce the original system to a three-DOFs one at a certain speed corresponds to the maximum energy. The eﬃciency of the TPOD method is veriﬁed via comparing with the bifurcation diagram of the original and reduced rotor system. The order reduction method provides qualitative analysis to study the reduced model of the high-dimensional rotor system.

Dynamical Balance and Verification of a Rotor System Based on Sensitivity Analysis

pp. 271-280 | DOI: 10.5890/JVTSD.2018.09.007

Zhong Luo, Yan-hui Wei, Xiao-jie Hou, Fei Wang

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Abstract

In allusion to the unbalanced vibration of rotor system, sensitivity analysis and balance method of rotor system were studied. Based on rotor dynamics, combined sensitivity analysis with the balancing methods of three trial weight and modal, a hybrid method was proposed which can be balanced without phase information. Firstly, the model of rotor was established by the ﬁnite element method and the correction plane is selected by the sensitivity analysis. Furthermore, the balance speed is determined according to the modal equilibrium theory and the weight calculation is conducted by the balancing method of three trial weight Finally, a dynamic balance experiment was carried out on the rotor model test station. The results of simulation and experiment show that the proposed balance method can not only eﬀectively reduce the residual vibration of rotor, but avoid the blindness of selecting the correction plane and balance speed by the traditional balance method, which is expected to improve the balance eﬃciency.

Multi-objective Optimization Design of Flap Sealing Valve Structure for Deep Sea Sediment Sampling

pp. 281-290 | DOI: 10.5890/JVTSD.2018.09.008

Guangping Liu, Yongping Jin, Youduo Peng, Buyan Wan

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Abstract

Taking the deep sea sediments air-tight sampler ﬂap seal valve as the research object, using the response surface method (RSM) and ﬁnite element analysis method to carry out the ﬂap sealing valve geometry design parameter optimization design research. First of all, a set of eccentrically set ﬂap seal valve is designed for the requirement of the pressurized seal of the marine deep sediment air-tight sampler, three-dimensional geometric model of the ﬂap seal valve is built using Solidworks.Then, The ﬂap sealing valve eccentricity angle θ , the valve cap upper end diameter D3, and the valve cover length l as the design variables, the bottom end opening diameter D5 of the valve body and the material strength under a given safety factor are set as constraints, the maximum stress value and weight of the ﬂap seal valve are set as optimization goals.The response surface model of the ﬂap sealing valve eccentricity angle θ , the valve cap upper end diameter D3, the valve cover length l and the ﬂap sealing valve maximum stress and weight is constructed. Finally, The geometrical structure parameters of the ﬂap sealing valve are optimized.

Inverse Problem for Degenerate Lotka-Volterra System of Three Equations

pp. 291-296 | DOI: 10.5890/JVTSD.2018.09.009

Varadharaj Dinakar, Krishnan Balachandran

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Abstract

We consider the degenerate Lotka-Volterra system with three equations in the linearized form. The internal observations with two measurements are allowed to obtain the stability result for the inverse problem consisting of simultaneously retrieving three coeﬃcients in the given parabolic system with the help of Carleman estimates for the degenerate Lotka-Volterra system.

JVTSD Volume 2, Issue 4

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On targeted energy transfer and resonance captures in the 2D-wing and nonlinear energy sinks

pp. 297-306 | DOI: 10.5890/JVTSD.2018.12.001

Wenfan Zhang, Jiazhong Zhang, Le Wang, Shaohua Tian

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Abstract

Targeted energy transfer, presented in two-dimensional wing coupled with two Nonlinear Energy Sinks (NESs) under freestream, is studied numerically, it is feasible to partially or even completely suppress aeroelastic instability by passively transferring vibration energy from the wing to the NES in a one-way irreversible fashion, and the relationship between the vibration suppression and Targeted Energy Transfer (TET) of the system is analyzed in detail. First, the model of the coupling system, which includes heave and pitch motions, is presented, and the NESs are located at the leading edge and trailing edge (NES1 and NES2) separately. Then, the vibrations suppressed by NESs are also investigated from the viewpoint of energy transfer etc., and the Resonance Captures (RCs) in the nonlinear coupling system are studied using spectrum analysis. Furthermore, the ensuing TET through the modes of wing (Heave and Pitch) and the NESs are discussed in detail. The results show that the NESs could absorb and dissipate a signiﬁcant portion of energy fed from the ﬂow to the wing, and the NESs could absorb the energy from every single motion of the wing, and the TET and RCs between modes can be more available in the coupling system. Therefore, the TET is more eﬃcient between the wing and NESs, and it leads to the increase of the critical velocity of freestream under which the nonlinear vibration of the wing can be suppressed by NESs eﬀectively.

Power Density – An Alternative Approach to Quantifying Fatigue Failure

pp. 307-326 | DOI: 10.5890/JVTSD.2018.12.002

Zachary T. Branigan, C. Steve Suh,

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Abstract

The power density theory is an alternate description of fatigue failure. It is derived from the concept of power density, which is physically equivalent to the amount of power deposited into a unit volume of the material experiencing dynamic loading. Power density results from changes in stress magnitude over time. All the stress alternations that occur across a broad bandwidth of frequencies contribute to the accumulation of power density. Higher frequencies coupled with faster changes in stress contribute more power density. Once this accumulation reaches a threshold – a fundamental property of the material – it is expected to fail by fatigue. The power density based methodology is applied to properly interpret the multiaxial vibration fatigue test results reported by Mrˇsnik, Slaviˇc and Bolteˇzar [15] using computer simulations. This serves as a feasibility study for the approach, as well as an example of how to apply it. The power density response of the system is analyzed, and the failure locations are predicted for each of the ten load cases that are considered. The predicted failure locations are in excellent agreement with the experimental results. Further examination of the approach would result in a better understanding of fatigue failure, thus improving engineering work across many industries.

Equilibrium points with their associated normal modes describing nonlinear dynam-ics of a spinning shaft with non-constant rotating speed

pp. 327-373 | DOI: 10.5890/JVTSD.2018.12.003

Fotios Georgiades,

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Abstract

In this article, the dynamics of a spinning shaft during spin-up/down operation, is examined analytically, around the equilibrium points. The system of equations of motion of a spinning shaft with nonconstant rotating speed has no linear part therefore the equilibrium points are rather essential. In the ﬁrst instance, the equilibrium points of the original system are determined. A restricted system is obtained by neglecting the rigid body angular position of the shaft, and the equilibrium manifold with its’ bifurcations is deﬁned. It is shown that this manifold, is formed by the backbone curve of the nonlinear normal modes which are associated with the rigid body angular motions of the spinning shaft. It is shown that all the equilibrium points of the original and the restricted system are degenerate. The original and restricted systems have been linearized around the equilibrium points, and examination of their stability through the eigenvalues of the Jacobian matrix showed that there are centres and unstable regions. Then, the frequencies and initial conditions of the normal modes of the linearized system around the equilibrium points are determined with the associated analytical solutions. The comparison of analytical with numerical results shows very good agreement, noting that the linearization around equilibrium is valid only for very small perturbations. This work is essential for understanding critical situations in the dynamics of the spinning shaft during spin-up/down operation, based on the associated normal modes. The stability analysis of the spinning shaft can be used further to identify regions with chaotic attractors, which should be considered for normal operation. Finally, considering other rotating structures with non-constant rotating speed, the equations of motion are similar to those of a spinning shaft. Therefore, the approach that is followed in this article can be considered as more general, and could be applied in all rotating structures during spin-up/down, and expecting similar results.

On Independent Period-m Evolutions in a Periodically Forced Brusselator

pp. 375-401 | DOI: 10.5890/JVTSD.2018.12.004

Albert C.J. Luo, Siyu Guo

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Abstract

In this paper, the analytical solutions of independent period-m evolutions (m=3,5,7,9) of chemical concentrations in a periodically forced Brusselator are obtained through the generalized harmonic balance method. Stability and bifurcation of independent periodic evolutions are determined through eigenvalue analysis. The nonlinear frequencyamplitude characteristics of independent periodic evolutions are discussed. To illustrate the analytical solutions, numerical simulations of stable and unstable period-m evolutions (m = 3,5,7,9) are presented herein. The harmonic amplitude spectrums give an approximate estimation of harmonic eﬀects on analytical solutions of periodic motions.

Experimental Validation of Damage Detection based on Member Axial-strain Mode Shapes for Truss Structures

pp. 403-416 | DOI: 10.5890/JVTSD.2018.12.005

Guirong Yan, Shirley J. Dyke and Ayhan Irfanoglu

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Abstract

In this study, a simple, eﬀective damage detection approach is proposed for truss structures to locate damage onto exact member(s) using vibration responses. First, a parameter that reﬂects the axial strain in truss members and is sensitive to local damage is proposed. This parameter is called the member axial-strain mode shape and can be extracted from the translational mode shapes. Each component in an member axial-strain mode shape is associated with a member, reﬂecting the axial strain in that member. Because damage to a member directly aﬀects the axial strain in that member, the proposed member axial-strain mode shape is an eﬀective parameter for evaluating the condition of truss members. Second, a damage indicator constructed by both member axial-strain mode shapes and natural frequencies are proposed. Experimental tests are conducted on a full-scale sign support truss to demonstrate the eﬀectiveness of the proposed approach. The results illustrate that the proposed approach can be applied to truss structures instrumented with a few accelerometers and using only response data.

JVTSD Volume 3, Issue 1

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Displacement Limiters as Instigators of Large Amplitude Vibrations in Lightly Damped Systems

pp. 1-8 | DOI: 10.5890/JVTSD.2019.03.001

Z.C. Feng, Yuyi Lin

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Abstract

Displacement limiters also known as stoppers are rigid barriers used to limit the motion or to alleviate the load in mechanical design. This paper identiﬁes conditions under which the stopper causes the motion to be trapped in large amplitude oscillations accompanied by violent impact with the stopper. Special focus is on those parameters for which the stopper was not expected to play any role based on the predicted linear steady-state responses.

Energy Harvesting Performance of Lead-free Piezoelectric Ceramics Bimorphs with Transverse Mode

pp. 9-22 | DOI: 10.5890/JVTSD.2019.03.002

Shang Wang, Turki Alghamdi, Zengmei Wang, and Fengxia Wang

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Abstract

Piezoelectric material has been extensively used in energy harvesting technologies. However, most commercially available piezoelectric materials, Pb [ZrxTi1-x] O3 (PZT), contains of more than 60 weight percent lead (Pb) [1]. Because of its extremely hazardous eﬀects of lead elements, there is a strong motive to substitute PZT by new lead-free materials with comparable properties to those of PZT. This paper tested three diﬀerent piezoelectric bimorphs, one is made by lead-free piezoelectric materials Barium Titanate (BaTiO3) (BT) and the other two are made from traditional Pb [ZrxTi1-x] O3 (PZT). Their output voltage and power were studied and compared when the cantilever bimorphs subjected to a tip or a base excitation. Equivalent circuit models of both lead free Ba-Tio3 and traditional PZT cantilevered piezoelectric energy harvester (Mech-PEH) were built in ANSYS APDL. The Finite Element (FEM) model was validated through comparing the output voltage and power with the experiment results. The energy harvesting performance of the lead free piezoelectric bimorph were compared with the same size high performance PZT bimorph via FEM analysis. The factors contribute to the piezoelectric material’s behavior were described. The output voltage and power were computed with the transient vibrations caused by plucking forces. Due to the complicated fabrication process of lead free piezoelectric samples, a typical quarter size samples were usually produced and examined by researchers before the mass production of formal rectangular shape bimorphs. Therefore, in this work, all bimorphs, including lead free Barium titanate (BaTiO3) (BT) and the other two types of PZTs, were composed of two quarter size circular ceramics and a rectangular substrate plate.

Inﬂuence of Duct Joint on Modal Parameters of Rectangular Duct

pp. 23-37 | DOI: 10.5890/JVTSD.2019.03.003

Nagaraja Jade, V. Nidheesh, B. Venkatesham

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Abstract

The present paper discusses inﬂuence of duct joint on structural dynamic characteristics (modal parameters) of a rectangular duct. An analytical model is developed to consider the eﬀect of duct joint on modal parameters. The joint condition is modeled as a combination of linear and torsional spring’s stiﬀness. Developed analytical model is validated with experimental results for a rectangular duct with Pittsburgh lock joint. It is observed that both natural frequencies and mode shapes are in good agreement. For further understanding the inﬂuence of duct joint on modal parameters, current analytical model results are compared to duct without joints results and noticed that only antisymmetric mode shapes of duct with joint condition are deviating from ideal duct.

Flow-induced Vibrations of two Staggered Circular Cylinders at Low Reynolds Number

pp. 39-53 | DOI: 10.5890/JVTSD.2019.03.004

Ze-Hua Ye, Xu Sun, Jia-Zhong Zhang

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Abstract

The eﬀect of ﬂow interference on the ﬂow-induced vibrations (FIVs) of two staggered circular cylinders at low Reynolds numbers is investigated using ﬂuid-structure interaction (FSI) simulations. The FIV mechanical model of the two staggered circular cylinders in a laminar ﬂow is proposed and the corresponding non-dimensional governing equations are presented. An FSI solution procedure is subsequently developed by combining the modiﬁed characteristic-basedsplit (CBS) ﬁnite element method, dual-time stepping method, segment spring analogy technique, generalizedα method and loosely-coupled partitioned method. The stability and accuracy of the procedures are validated using a benchmark FSI problem concerning the FIVs of a single circular cylinder in a laminar ﬂow. Finally, using the numerical method proposed, the FIVs of two staggered circular cylinders at Re = 200, T/D (space ratio) = 5∼7 and α (inclined angle of the line connecting the two cylinders centers) = 0o ∼90o are computed, and the eﬀects of T/D and α on the vortex structure, ﬂuid load and FIVs are discussed in detail.

On Experimental Periodic Motions in a Duﬃng Oscillatory Circuit

pp. 55-70 | DOI: 10.5890/JVTSD.2019.03.005

Yu Guo, Albert C.J. Luo, Zeltzin Reyes, Abigail Reyes, Rojitha Goonesekere

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Abstract

In this paper, the dynamics of a Duﬃng oscillatory system are studied through both an experimental method and analytical predictions. A Duﬃng oscillatory circuit is built and experimental data of various periodic motions are obtained. The semi-analytical method using discrete implicit maps is adopted to determine such periodic trajectories analytically using the same parameters as in the experiments. Finally, illustrations of various periodic motions on both trajectories and harmonic amplitudes are demonstrated between the experimental data and analytical predictions. From the current experimental technology, experimental results may not provide real results in nonlinear dynamical systems.

Periodic Motion for an Oblique Impact System with Single Degree of Freedom

pp. 71-89 | DOI: 10.5890/JVTSD.2019.03.006

Xiaowei Tang, Xilin Fu, Xiaohui Sun

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Abstract

Oblique impact is a common phenomenon in engineering. The appearance of oblique impact will make the system strongly nonlinear and nonsmooth. In this paper, the period N−n motion of an oblique impact system with single degree of freedom is investigated by the theory of discontinuous dynamical system. The analytical conditions for the existence and local stability of the period N−n motion are obtained. All of these are under the assumption that the mass moved with very small angular amplitude. Once such an assumption was not true, the method above would be invalid. The discrete mapping method is used to solve this problem. The analytical conditions for the existence, the local stability of the period N−n motion are given through the discrete mapping method. The numerical simulation shows that the oblique impact will make the dynamic behavior of a single degree of freedom system more complex.

The Trajectory Tracking Control of ﬁxed-wing UAV with Self-organizing Fuzzy Neural Network to Identify and Compensate the Modelling Uncertainties

pp. 91-106 | DOI: 10.5890/JVTSD.2019.03.007

Yu Tang, Lijia Cao, Da Lin

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Abstract

Firstly, the dynamics model of ﬁxed-wing UAV is given in the paper and an adaptive controller of the mode is designed based on dynamic inversion method, then a compensation strategy called SFNN-RC based on the self-organizing fuzzy neural network techniques and a robust controller is designed to online identify and compensate the modeling uncertainty part of ﬁxed-wing UAV system in trajectory tracking control process. The robust controller in SFNN-RC is presented to optimize the convergence performance of the self-organizing fuzzy neural network. The stability of the SFNN-RC method can be proved based on Lyapunov theory. To demonstrate the eﬀectiveness of the proposed method, some simulation results are illustrated in this paper.

JVTSD Volume 3, Issue 2

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Parametric Model for Photovoltaic Cells with Bypass Diodes Under Partial Shading

pp. 109-119 | DOI: 10.5890/JVTSD.2019.06.001

Z. C. Feng, Stephen J. Lombardo

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Abstract

We study the disproportional eﬀect of non-uniformity on a system of photovoltaic cell network. When a cell is partially shaded, besides the loss from the shaded cell, the power output of the whole cell network is signiﬁcantly aﬀected. Although this eﬀect is well known in the solar cell community, the theoretical analysis has relied on one or more approximations or specially deﬁned functions. In this paper, we present a parametric formulation of photovoltaic cells in which the output voltage and current relationships are described by explicit functions parametrized by the voltage over the cell diode. No additional approximations or specially deﬁned functions are required to study the output characteristics. We further show that the model remains unchanged when applied to a network of many identical PV cells either in parallel or in series; the parameters for the network can be obtained from those of the cell. Incorporating interpolation in calculation, the model can be used to study a network with dissimilar cells, speciﬁcally a network with a partially shaded cell. We show that the voltage over the shaded cell becomes negative and power is dissipated over the shaded cell. The model is also conveniently used to study the network output characteristics when bypass diodes are included in the PV network.

The City of Lubbock is Running Away. Integration and Isolation Patterns in the Wandering City

pp. 121-132 | DOI: 10.5890/JVTSD.2019.06.002

Dimitri Volchenkov, Veniamin Smirnov

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Abstract

We propose computationally feasible statistical algorithms for the automated assessment of isolation and integration of urban locations and neighborhoods by using maps acquired from the Open Stree Map service. Integration and isolation deﬁned by observing the properties of scale-dependent random walks on city street maps are not always opposites. While isolation worsens economic and social mobility prospects in sprawling metropolitan areas, some secluded places homing the wealthiest can be characterized as being in integrated isolation in the city.

Modiﬁed Harmonic Balance Method for Solving Nonlinear Free Vibration Problem of Beam Resting on Nonlinear Elastic Foundation

pp. 133-145 | DOI: 10.5890/JVTSD.2019.06.003

M. Saifur Rahman, Ahmed Hossain

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Abstract

Free vibration of beam is an important issue in structural engineering because of its various physical applications in the real ﬁeld. In this paper, the free vibration of a nonlinear beam rest on a nonlinear elastic foundation is studied. A mathematical modeling for the free vibration of beam rest on nonlinear elastic foundation is presented. A modiﬁed harmonic balance is used to investigate the nonlinear free vibration response of beam. The main advantage of the method is that the unknown coeﬃcients are expressed in power series of a new parameter. However, in a classical harmonic balance method the values of the unknown coeﬃcients are determined by solving a set of complicated algebraic equations truncating higher order nonlinear terms. The results obtained by the proposed method have been compared with corresponding numerical results to verify the accuracy of method. Besides, the eﬀects of various elastic foundation coeﬃcients have been examined.

On Stability and Bifurcation of Equilibriums in Nonlinear Systems

pp. 147-232 | DOI: 10.5890/JVTSD.2019.06.004

Albert C. J. Luo

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Abstract

In this paper, a local theory for stability and bifurcation of equilibriums for nonlinear dynamical systems is presented. The stability and bifurcation on speciﬁc eigenvectors of the linearized system at equilibrium is discussed. The higher-order singularity and stability for nonlinear systems on the speciﬁc eigenvectors are developed. The Hopf bifurcation based on the transformation of the Fourier series base is also discussed. The stability and bifurcation of equilibriums in low-dimensional dynamical systems is discussed for a better understanding of stability and bifurcation theory. The Lyapunov function stability is brieﬂy discussed, and the extended Lyapunov stability theory is presented.

Corrigendum/Addendum in ‘Georgiades, F., 2018, Equilibrium Points with Their Associated Normal Modes Describing Nonlinear Dynamics of a Spinning Shaft with Non-Constant Rotating Speed, Journal of Vibration Testing and System Dynamics, 2(4), 327-373’

pp. 233-235 | DOI: 10.5890/JVTSD.2019.06.005

Fotios Georgiades

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Abstract

The form of the lower part of the vector ﬁeld erroneously leads to the conclusion/statement that the original system in 1st order has no linear counterpart, which is untrue. In here, the decomposition to linear and nonlinear part of the 1st order original system it is shown. The eigenvalues of the matrix associated with the linear part are all zero, therefore it cannot be claimed Lyapunov’s conclusion that the system in low energies can be approximated with the linear counterpart. Also, two typographic errors have been corrected. The corrections and the additions not only don’t aﬀect the value of the rest part of the published article but also enhance the value of the original manuscript. More precisely, since the original system in low energies cannot be approximated by the solution of the linear counterpart, the followed approach to describe the dynamics of the spinning shaft with linearization around the equilibria of the restricted system which are the rigid body motions, is of higher signiﬁcance.

JVTSD Volume 3, Issue 3

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Non-classical Natural Frequency Analysis of Piezoelectric Cylindrical Nano-shell with Surface Energy Eﬀects

pp. 237-258 | DOI: 10.5890/JVTSD.2019.09.001

Sayyid H. Hashemi Kachapi

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In this paper, the size-dependent eﬀect on the free vibration analysis of cylindrical piezoelectric nano-shell with arbitrary boundary conditions is studied. The cylindrical piezoelectric nano-shell is modeled based on Gurtin-Murdoch surface elasticity theory and the linear Von-Karman- Donnell’s strain-displacement. Also, the assumed mode method is used for changing the partial diﬀerential equations into ordinary diﬀerential equations. A variety of new vibration results including frequencies and mode shapes for piezoelectric cylindrical nano-shell with non-classical restraints as well as diﬀerent material parameters are presented, which may serve as benchmark solution for future researches. The convergence, accuracy and reliability of the current formulation are validated by comparisons with existing experimental and numerical results published in the literature, with excellent agreements achieved.

A Period-1 Motion to Chaos in a Periodically Forced, Damped, Double-Pendulum

pp. 259-280 | DOI: 10.5890/JVTSD.2019.09.002

Albert C.J. Luo, Chuan Guo

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Abstract

In this paper, periodic motions in a periodically forced, damped double pendulum are analytically predicted through a discrete implicit mapping method. The implicit mapping is developed from discretization of the corresponding diﬀerential equation. From the mapping structures, period-1 to period-4 motions are obtained and the corresponding stability and bifurcation analysis of the periodic motions are completed through eigenvalue analysis. Using the ﬁnite Fourier series, nonlinear frequency-amplitude characteristics of period-1 to period-4 motions are presented. Numerical simulations of period motions in the double pendulum is completed, and the initial conditions are obtained from the analytical predictions. The harmonic amplitude spectrums are also presented for showing harmonic term eﬀects on periodic motions.

Study of Routes to Chaos in Vibroimpact System with Continuous Wavelet Transform

pp. 281-296 | DOI: 10.5890/JVTSD.2019.09.003

V. A. Bazhenov, O. S. Pogorelova, T. G. Postnikova

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Abstract

The study of dynamical systems chaotic behavior and their routes to chaos was in particular attention at recent years. These phenomena study in non-smooth dynamical system is of the special scientists’ interest. We apply the Continuous Wavelet Transform (hereinafter - CWT) to investigate the intermittent route to chaos, boundary crisis, and transitional regimes under quasi-periodic route to chaos in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We show that CWT application is very useful to observe the intermittency, chaos and transitional regimes. It allows one to detect and to determine these phenomena with great conﬁdence, reliability, and clearness.

A Regulated Market Under Sanctions: On Tail Dependence Between Oil, Gold, and Tehran Stock Exchange Index

pp. 297-311 | DOI: 10.5890/JVTSD.2019.09.004

Abootaleb Shirvani, Dimitri Volchenkov

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Abstract

We demonstrate that the tail dependence should always be taken into account as a proxy for systematic risk of loss for investments. We provide the clear statistical evidence of that the structure of investment portfolios on a regulated market should be adjusted to the price of gold. Our ﬁnding suggests that the active bartering of oil for goods would prevent collapsing the national market facing the international sanctions.

A New Fault Locating Algorithm for T-splice Transmission Lines based on Back-ward Traveling Wave

pp. 313-328 | DOI: 10.5890/JVTSD.2019.09.005

Hao Wu, Xingxing Dong, Qiaomei Wang

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Abstract

Existing fault locating algorithms for T-splice transmission lines are hugely susceptible to traveling wave velocity. To address this issue, this paper presents a new fault locating algorithm for T-splice transmission lines based on the initial voltage backward traveling wave. In this algorithm, the three-terminal busbar initial voltage backward traveling waves are collected and S-transform is implemented to analyze the ratio of voltage amplitude and construct discriminant of the faulted transmission line. Once the faulted branch is detected, three-terminal line is converted into two-terminal line. The fault range locating algorithm can be developed by using line parameters and the time initial traveling wave used to reach the three-terminal busbar. The algorithm making it less susceptible to swing amid the uncertainty of traveling wave velocity and overcomes the shortcomings of the unreliability of traditional method for detecting the faulted line near T node. Simulation results demonstrate high accuracy of the algorithm, which is less susceptible to the changes in fault types, transitional resistances, initial fault angles and other factors.

Problems of Size Eﬀect in Similar Experimental Models: A Review

pp. 329-346 | DOI: 10.5890/JVTSD.2019.09.006

Si-wei Guo, Zhong Luo, Qing-wen Yu, Fei Wang

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Abstract

This paper is concerned with a review of the size eﬀect involved in the similar experimental models. The review covers in many ﬁelds, including size eﬀect in microscopic system structure such as the study of the micro-beam mode, civil structure and mechanical structure such as the study of mechanical properties, the application of dynamic similarity model design in large structures. This is followed by the inﬂuencing factors of size eﬀect and methods of predicting fatigue strength and fatigue life of large structures. Analysis of formulas for predicting the stress and strain, stress ﬁeld near notched specimens used in large structures are established. Finally, the formulas for predicting the size factor and fatigue life of large structures about size eﬀect are summarized and prospected.

The Global Analysis of Equilibrium Stability in 1-dimensional Systems

pp. 347-367 | DOI: 10.5890/JVTSD.2019.09.007

Albert C. J. Luo

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Abstract

In this paper, a global analysis of equilibrium stability in 1-dimensional nonlinear dynamical systems is presented. The classiﬁcation of dynamical systems is given ﬁrst, and inﬁnite-equilibrium systems are deﬁned. The 1-dimensional dynamical systems with a single equilibrium are discussed. The 1-dimensional dynamical systems with two and three equilibriums are discussed. Simple and higher-order equilibriums in 1-dimensional dynamical systems are analyzed, and a higherorder equilibrium is an equilibrium with higher-order singularity. The ﬂows of equilibriums in 1-dimensional systems in phase space are illustrated for a better understanding of the global stability of equilibriums in 1-dimensional dynamical systems.

Addendum in ‘Silva, Vin´ıcius B. et al., 2018, A new application of the normal form description to a N-dimensional dynamical systems attending the conditions of a Hopf bifurcation, Journal of Vibration Testing and System Dynamics, 2(3), 249-256’

pp. 369-371 | DOI: 10.5890/JVTSD.2019.09.008

Vin´ıcius B. Silva, Jo˜ao P. Vieira and Edson D. Leonel

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In the underlying work, a general theorem for the derivation of the normal form of N-dimensional systems reduced to its center manifold is proposed and proved. In the present addendum, some observations regarding the conditions of the theorem are added. The corrections and the additions not only don’t aﬀect the value of the best part of the published article but also enhance the value of the original manuscript.

JVTSD Volume 3, Issue 4

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Bifurcation of the Equilibria of a Cylinder in a Steady Two-dimensional Channel Flow

pp. 373-389 | DOI: 10.5890/JVTSD.2019.12.001

Zachary J. Lipira, Z. C. Feng

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Abstract

The flow about a circular cylinder placed within a channel is studied numerically in order to examine the lift forces on the cylinder for Reynolds numbers below the onset of unsteady flow. It is observed that there is a critical Reynolds number between 60 and 80 that results in the lift force to become destabilizing for the cylinder equilibrium position at the center of the channel. Meanwhile, two new equilibrium positions of the cylinder away from the channel center come to existence. Associated with this bifurcation of the equilibria, the flow streamline and vorticity plots are presented.

Application Research of Artificial Intelligence Technology in Chinese Baijiu Brewing

pp. 391-402 | DOI: 10.5890/JVTSD.2019.12.002

Guiyu Zhang, Xianguo Tuo, Wanchun Tian, Qiang Han, Fan Tao

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Abstract

This study first constructed the information system, and monitored the key technical parameters of the brewing process in real time. The neural network was used to construct the fermented grains model, and the online evaluation of the fermentation process was realized according to the real-time fermentation parameters. The intelligent batching system adjusted the ratio of the fermented grains, grains and other materials according to the evaluation result. The robot used infrared thermal imaging technology to perform the steamerfilling operation. The application results showed that the technology had a positive effect on improving the yield and quality of Chinese Baijiu.

The Stability and Bifurcation of Equilibriums in Low-degree Polynomial Systems

pp. 403-451 | DOI: 10.5890/JVTSD.2019.12.003

Albert C. J. Luo

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Abstract

In this paper, the stability and bifurcation of equilibriums in low- degree polynomial systems are discussed. Appearing and switching bifurcations of simple and higher order equilibriums are discussed, and such bifurcations of equilibriums are not only for simple equilibri- ums but for higher-order equilibriums. The 3rd-order sink and source bifurcations for simple equilibriums are presented. The 3rd-order sink and source switching bifurcations for saddle and nodes are discov- ered, and the 4th-order upper-saddle and lower-saddle switching and appearing bifurcations are obtained for two 2nd-order upper-saddles and two 2nd-order lower-saddles, respectively. Graphical illustrations of global stability and bifurcations are presented.

Entire Flow Field Modeling Including Wake Region through Improved Finite-State Method

pp. 453-468 | DOI: 10.5890/JVTSD.2019.12.004

Jian-Zhe Huang, David Peters

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Abstract

In the recent decades, the accuracy and robust of finite state inflow model to provide the velocity on the disk have been greatly improved. It is adequate to compute the thrust, pitch and roll moment real time for normal flight conditions. For lifting rotor flying close to a non-penetrable surface, the wake will interact with the inflow of the lifting rotor. Additionally, for co-axial rotors the wake of the upper rotor influences the lower rotor. Therefore, it is necessary to develop a model to compute the flow field in the wake since the Peters-He model cannot give the induced velocity below the rotor disk. In this paper, the improved finite state model will be introduced to compute the axial induced velocity everywhere in the flow field including wake and downstreamregions. The adjoint theorem will be introduced, and the computational efficiency of the convolution method and numerical algorithm for computing the adjoint varibales with time delay will be compared. With the parameters of a Harrington rotor, the results in the time domain for such a rotor in hover and forward flight conditions will also be illustrated.

A Novel Decision-Making Framework for Probabilistic Search

pp. 469-480 | DOI: 10.5890/JVTSD.2019.12.005

Liang Yu, Yongchun Liu, Da Lin

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Abstract

In this paper, we present the search problem formulated as a decision making problem, the search agent decides whether the target is present in the search region, and if so, where it is located. Then we propose a sequential decision-making framework for a search agent to find a lost target within a bounded region with the searcher motion constraints and imperfect observations being considered. This framework enables the theoretical study to the evolution of the search decision, then we propose two effective adaptive search strategies, which have the advantage of requiring less computation than traditional search strategy. Simulation results shows that the proposed adaptive search strategies have a better performance. Finally, the proposed control strategies are analyzed from different perspectives in detail.

Study on Fractional Differential Equations via Atangana-Baleanu Fractional Derivative

pp. 481-487 | DOI: 10.5890/JVTSD.2019.12.006

S. Harikrishnan, K. Kanagarajan, D. Vivek

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Abstract

In this note, we establish the existence, uniqueness and stability of a special class of fractional pantograph equation with Atangana- Baleanu fractional derivative(ABFD). The arguments are based upon Schauder fixed point theorem and Banach contraction principle. In addition, we discuss the stability results of proposed equation by the concept of Ulam. At last an example is given to illustrate the theory.

JVTSD Volume 4, Issue 1

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The Stability and Bifurcation of the (2m)th-degree Polynomial Systems

pp. 1-42 | DOI: 10.5890/JVTSD.2020.03.001

Albert C. J. Luo

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Abstract

In this paper, the global stability and bifurcations of equilibriums in the (2m)th-degree polynomial system are discussed for a better understanding the complexity of bifurcations and stability of equilibriums. The appearing and switching bifurcations for simple equilibriums are presented, and the appearing and switching bifurcations for higherorder equilibriums are discussed as well. The teethcomb-appearing, spraying-appearing, andsprinkler-spraying-appearing bifurcations for simple and higher-order equilibriums are presented. The antennaswitching bifurcations for simple and higher-order equilibriums are discussed and the parallel straw-bundle-switching and ﬂower-bundleswitching bifurcations for simple and higher-order equilibriums are presented as well.

Application of Bayesian Decision Tree Algorithm in Breast Cancer Prediction

pp. 43-49 | DOI: 10.5890/JVTSD.2020.03.002

Yang Xiang, Lin-Lu Dong, Hong Song, Kun-jian Yu

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Abstract

Aiming at the low classiﬁcation accuracy of common decision tree C4.5 algorithm and the condition attribute problem of decision tree splitting point, a Bayesian decision tree algorithm combining ordinary decision tree C4.5 algorithm and naive Bayesian correlation algorithm is proposed in this paper. On this basis, the consistency test coeﬃcient(kappa coeﬃcient) is introduced to improve the correlation algorithm in the information gain rate in C4.5. Finally, the newly generated decision tree is pruned according to the most suitable splitting point. The improved algorithm proposed in this paper has a distinct improvement compared with the algorithm proposed in other literatures considering both time and accuracy.

Dynamic Characteristics Analysis of Rotor-Bearing System and Experimental Validation

pp. 51-63 | DOI: 10.5890/JVTSD.2020.03.003

Jiarong Liu, Zhong Luo, Zhe Ding, Jinwen Wang

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Abstract

As for the vibration problem of rotor system for large rotating machinery such as aero engines, a ﬁnite element model for dynamic similarity experiment system of rotor is established based on ﬁnite element theory. The eﬀect of support stiﬀness and support position on the dynamic characteristics of the rotor system have been emphatically analyzed. Moreover, the eﬀect of support stiﬀness on the dynamic characteristics of rotor system have been veriﬁed on the designed test rig. The results show that, under diﬀerent support stiﬀness intervals, each order natural frequency of the rotor system has a diﬀerent variation tendency with the support stiﬀness or position. In addition, the variation of the mode shapes with the support stiﬀness or position are closely related to the variation of the natural frequencies with the support stiﬀness and position. Combining with the practice, the natural frequencies of the rotor system can be reasonably designed and the harmful mode shapes can be avoided by adjusting the supporting characteristics of the rotor system.

Viscous and Ohmic Heating Eﬀects on MHD Flow of Nanoﬂuid Past a Porous Stretching Sheet with Thermal Radiation and Heat Generation/Absorption: Copper-Alumina Water

pp. 65-78 | DOI: 10.5890/JVTSD.2020.03.004

M. Thiagarajan, M. Dinesh Kumar

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The important focus of this work is to numerically examine the viscous dissipation and Ohmic heating eﬀects on hydromagnetic ﬂow of nanoﬂuid over a porous stretching sheet with thermal radiation and heat generation/absorption ﬁlled with water-based copper and alumina nanoﬂuids. Heat transfer features are investigated through convective conditions. Consider steady, nonlinear, two-dimensional of an incompressible, viscous and electrically conducting ﬂuid past a porous stretching sheet in the presence variable magnetic ﬁeld. To obtain meaningful results, we have taken thermal radiation in the heat transfer procedure. Governing nonlinear partial diﬀerential equation and they are transformed into an ordinary diﬀerential equation by using similarity transformation and the numerical solution is obtained by using Nachtsheim-Swigert shooting iteration scheme together with a fourth order Runge-Kutta integration method. Numerical results are obtained for the velocity and the temperature in the boundary layer region is studied in elaborate. Quantities of engineering interest such as skin friction coeﬃcient and nusselt number are also obtained numerically and are tabulated.

Analysis of Mass Transport in a Turbulent Flame Using Lagrangian Coherent Structures

pp. 79-93 | DOI: 10.5890/JVTSD.2020.03.005

Shengli Cao, Jiazhong Zhang, Yoshihiro Deguchi, Nannan Dang, Shaohua Tian

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Abstract

The premixed piloted turbulent ﬂame is studied numerically using Lagrangian coherent structures (LCS) to study and analyze the masstransport process from the viewpoint of nonlinear dynamic systems. The mass transport is shown to demonstrate a rich dynamical behavior. Firstly, the numerical simulation results show that the boundaries in the combustion ﬁeld are delineated by the Lagrangian Coherent Structures. Secondly, the distribution of the attracting LCSs and the OH radical are compared to study the surface of the ﬂame. Finally, the evolution of the LCS was tracked to analyze the vortexes and mass transport near the burner. The results show that the attracting LCS can be considered as a surface of the turbulent ﬂame near the burner. The serial vortexes are regularly generated near the piloted jet, and they are gradually stretched and folded. These vortexes are attracted by the main jet as they move downward in the ﬂow. The main jet goes into the ﬂow ﬁeld following an attracting LCS and moves forward attracting the piloted jet and the co-ﬂow. However, ﬂuid in the mainstream region has never entered into the piloted jet region, and this region does not exchange substance with the co-ﬂow region. If the ﬂow speed increases, air from the co-ﬂow may pass through the LCS to mix with the material from the piloted jet region. Application of the LCS technique to study mass transport processes provides a new viewpoint for analyzing premixed piloted turbulent ﬂames.

JVTSD Volume 4, Issue 2

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The Stability and Bifurcation of the (2m+1)th-Degree Polynomial Systems

pp. 95-146 | DOI: 10.5890/JVTSD.2020.06.001

Albert C J Luo

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Abstract

In this paper, the global stability and bifurcations of equilibriums in the (2m+1)th -degree polynomial system are discussed for a better understanding of the complexity of bifurcations and stability of equilibriums in such a (2m+1)th-degree polynomial system. The appearing and switching bifurcations for simple and higher-order equilibriums are presented. The broom-teethcomb-appearing, broom-spraying appearing, and broom-sprinkler-spraying-appearing bifurcations for simple and higher-order equilibriums are presented. The antennaswitching bifurcations for simple and higher-order equilibriums are discussed, and the parallel straw-bundle-switching and ﬂower-bundleswitching bifurcations for simple and higher-order equilibriums are also presented.

Decision Making for a Sustainable and Rentable Maintenance of a TORNADO Gas Turbine based on Fuzzy Logic Concept

pp. 147-162 | DOI: 10.5890/JVTSD.2020.06.002

Bachir Alili, Ahmed Hafaifa, Mouloud Guemana, Lakhdar Mazouz

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Abstract

In the modern oil & gas industry ,speciﬁcally, in hydrocarbon transportation by pipelines, maintenance decision making for the functional availability of equipment has a major inﬂuence on the profitability of the facilities. In this perspective, this work aims to increase the capacity to monitor the behavior of a TORNADO type gas turbine, installed at an oil pumping station in Hassi R’Mel situated in southern Algeria, with modeling the degradation actions of this machine to make the eﬀective decisions of their maintenance. The maintenance decision support process proposed in this work is based on the concept of fuzzy logic, helps the maintenance operator to choose the most appropriate maintenance actions depending on availability, productivity and quality of the transported oil. This minimizes costs and environmental impact, by ensuring an optimal level of oil transportation, for the monitoring of examined turbine component failures with a sustainable and cost-eﬀective maintenance strategy.

Application of CNN-ATTBiLSTM Hybrid Algorithm in Natural Language Processing

pp. 163-172 | DOI: 10.5890/JVTSD.2020.06.003

Yang Xiang, Hong Song

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Abstract

Aiming at the problems that traditional machine learning algorithms such as SVM rely too much on emotional dictionary, grammatical mechanism and low recognition rate in processing text sentiment by natural language, a diﬀerent ratio CNN-ATTBiLSTM algorithm based on the algorithm is proposed in this paper. First, the CNN algorithm is used to process the local features, and the CNN feature fusion method is used to integrate ATTBiLSTM (two-way long-term and short-term memory network based on attention mechanism) at the output, Then the two algorithms are combined in diﬀerent ratios to ﬁnd the highest F1 value as the combination ratio. Finally, the algorithm proposed in this paper is compared with the traditional machine learning algorithms and the proposed algorithms in the experimental data set. The results show that the new algorithm is 0.85% better than the equal weight ratio CNN-ATTBiLSTM algorithm. So it is the best algorithm compared with other algorithms.

Directional Sensing in Insect Vibration Communication and Reconstruction of Zhang Heng’s Seismoscope

pp. 173-181 | DOI: 10.5890/JVTSD.2020.06.004

Z.C. Feng

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Abstract

This work is motivated by ﬁnding dynamic quantities by which some insects are able to sense the direction of vibration sources. Many insects communicate by substrate vibrations alone. We introduce a two-degree-of-freedom dynamic model with time delay in the inputs to the system. Through frequency response functions we obtain surprisingly simple results with regard to the vibrational responses to waves from two opposite directions. The two-degree-of-freedom systems are divided into two types. For those whose rotational resonance frequency is lower than the translational resonance frequency, type I, the vibration on the side toward the wave source is larger than the back side for all wave frequencies. This diﬀerence in vibration amplitudes reverses for those systems whose rotational resonance frequency is above the translational resonance frequency – type II. This directional dependence is further demonstrated by numerical simulations of bandlimited random input. Our results provide the basic principle guiding the reconstruction of“Seismoscope”that was recorded to have been invented by Zhang Heng in ancient China before 132AD.

An Improved Algorithm of Edge Detection for Aircraft Positioning

pp. 183-190 | DOI: 10.5890/JVTSD.2020.06.005

Lin-Lu Dong, Zhi-Shuang Xue, Liang-Jun Zhao, Xiao-Shi Shi

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Abstract

The method of aircraft positioning in the anti-UAV(unmanned aerial vehicle, UAV) system is detecting objects through an image. Its preprocessing process needs to extract the edge of the target aircraft, however, due to the inﬂuence of image acquisition technology and electromagnetic environment, the obtained aircraft image is often interfered by a lot of noise. The traditional edge detection algorithm and the method of using local uniform sparsity to enhance the features of the aircraft can not meet the engineering requirement of detecting the edge of the aircraft which has complex structure. Aiming at this problem, an algorithm of edge extraction for aircraft under strong noise is proposed. Firstly, searching high deﬁnition images of other aircrafts similar to the structure of the target aircraft in the database, the algorithm is used to learn the texture features of these images. Then, the missing texture features corrupted by strong noise are repaired, this process can achieve the goals of enhancing the target aircraft’s detail features and weakening inﬂuence of the background’s features. Finally, the edge of the target aircraft is successfully detected. The experimental results show that the proposed algorithm can eﬀectively detect the edge of the aircraft under strong noise.

Energy Harvesting from Quasiperiodic Vibrations in a Delayed Rayleigh-Duﬃng Harvester Device

pp. 191-200 | DOI: 10.5890/JVTSD.2020.06.006

Amine Bichri, Ilham Kirrou, Mohamed Belhaq

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Abstract

This paper studies quasiperiodic vibration-based energy harvesting in a delayed Rayleigh-Duﬃng oscillator coupled to a piezoelectric harvester device. Analytical investigation is performed using the multiple scales method to obtain approximation of periodic and quasiperiodic responses as well as the corresponding output power. The inﬂuence of diﬀerent parameters of the harvester on the amplitude of solutions and powers is examined. Results show that for appropriate values of the delay parameters, quasiperiodic vibration-based energy harvesting is signiﬁcantly improved far from the resonance while the periodic vibration-based one is almost absent near the resonance.

JVTSD Volume 4, Issue 3

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Bifurcation Trees of Period-1 to Period-2 Motions in a Periodically Excited Nonlinear Spring Pendulum

pp. 201-248 | DOI: 10.5890/JVTSD.2020.09.001

Albert C.J. Luo, Yaoguang Yuan

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Abstract

The spring-pendulum system has been of greet interest for a long time, and one tried to use the perturbation analysis to understand such a system. Until now, one cannot provide a satisﬁed result to explain the dynamics of the spring-pendulum system. In this paper, bifurcation trees of period-1 to period-2 motions in a periodically forced, nonlinear spring pendulum system are obtained through the discrete mapping method. The corresponding harmonic frequency amplitude characteristics of period-1 to period-2 motions are presented, and the stability and bifurcations of period-1 to period-2 motions on the bifurcation trees are presented as well. From the analytical prediction, numerical illustrations of period-1 and period-2 motions are completed for comparison of numerical and analytical solutions. The results presented in this paper are totally diﬀerent from the traditional perturbation analysis.

A Subgrid Stabilized Method for Lid-driven Cavity Flow at Higher Reynolds Number

pp. 249-258 | DOI: 10.5890/JVTSD.2020.09.002

Yamiao Zhang, Langhuan Lou, Jiazhong Zhang, Yongshen He

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Abstract

A subgrid stabilized method based on two local Gauss integrations is presented to the numerical simulation of 2-D steady incompressible lid-driven cavity ﬂow at higher Reynolds numbers. The main idea of this method is to use the subgrid model based on two local Gauss integrations as a stabilized term on the ﬁnite element discretization. In this method, the discretization equation is solved by Oseen iterative scheme. It is shown that steady ﬂow simulations of the lid-driven cavity problem are computable up to Re = 45000. This maximum Reynolds number has not been reached by other stabilized ﬁnite element methods reported. Moreover, the computed vorticity values at the center of the primary vortex agree well with previous analytical solutions in the limit of inﬁnite Reynolds number, and the numerical results for the properties of the primary vortex and the velocity components are also in agreement with the benchmark data in earlier studies.

A Novel Method for Denoising the Image with Nuclear Radiation Noise

pp. 259-268 | DOI: 10.5890/JVTSD.2020.09.003

Lin-Lu Dong, Zhi-Shuang Xue, Xiao-Fang Liu, Xiao-Shi Shi

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Abstract

In the environment of severe nuclear radiation, remote operation often uses a camera to transmit pictures to the control room. Because the noise generated by the current electronic equipment under the interference of nuclear radiation is random and irregular, the traditional denoising methods cannot meet the requirement of denoising noisy image eﬀectively. Aiming at this problem, a denoising method based on image restoration technology is proposed. Firstly, some representative images are intercepted from the video of actual nuclear radiation ﬁeld as experimental objects. Then these images are smoothed to get the region A where the pixel diﬀerence between the noisy mage and the smoothed image is larger than the threshold and the region B where the pixel diﬀerence between the smoothed image and the clean image is greater than the threshold to form two regions to be restored. Finally, the process of image restoring is performed on the two regions respectively. The two images after restoration are fused to obtain the ﬁnal image. The experiment shows that our method has good performance in protecting the details of the image while removing the nuclear radiation noise. Compared with other methods, our method can obtain a more clear image.

Mathematical Validation of Power Loss due to Mechanical Vibration in Rotating Equipment

pp. 269-278 | DOI: 10.5890/JVTSD.2020.09.004

Mukesh A Bulsara†, Ruship Trivedi

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Abstract

Rotating equipment like pump, blower, fan etc. are widely used in industries, where high vibration levels are observed speciﬁcally caused due to unbalance in rotating parts. A survey of literature has shown that, in spite of growing concerns about the eﬀect of vibration levels on the power consumption, little research has been done to correlate the vibration level with power loss due to vibration. In a large reﬁnery, with hundreds of pumps and motors, the wasted power cost, due to vibrations alone may run into thousands of dollars. The objective of this work is to propose a systematic mathematical analysis to predict the eﬀect of unbalance on the power loss in a rotor-shaft system and validate with experiments performed on a laboratory setup at diﬀerent speeds. It is observed that as rotational speed and degree of unbalance is increased, power consumption also increases. Power loss due to diﬀerent degree of unbalance viz 60 gm.cm, 120 gm.cm and 180 gm.cm was measured experimentally on a test setup comprising of rotor-shaft system and mathematical validation is presented for the same. Power loss mainly takes place due to friction in bearings, which is attributed to centrifugal force produced by unbalance and displacement of rotor-shaft system. Calculated power loss is in close range of power loss determined experimentally.

The Roles of Mercury in Intracytoplasmic Sperm Injection

pp. 279-286 | DOI: 10.5890/JVTSD.2020.09.005

Z. C. Feng, Howard H. Hu, Yuksel Agca

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Abstract

Intracytoplasmic sperm injection (ICSI), microinjection of a single spermatozoon into an oocyte, is a routine procedure in assisted reproduction programs. This procedure uses ﬁne control of small bore microinjection needles and precise volume control via hydraulic syringe pumps. In many early experiments mercury is placed within the injection system because its high surface tension in the system facilitates the injection procedure. However, mercury is cytotoxic and therefore alternative ﬂuids or approaches are needed. Here we examine the main properties of mercury and their impact on the various aspects of ICSI. We conclude that the small momentum diﬀusivity of mercury is the most important contributing factor that facilitates the ICSI procedures.

Comparing Diﬀerent Theories for Dynamic Behavior of a Functionally Graded Beam

pp. 287-296 | DOI: 10.5890/JVTSD.2020.09.006

Peyman Beiranvand, Matin Abdollahifar, Farzad Akbarinia

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Abstract

Theoretical formulation, Navier’s solutions of rectangular plates based on a new higher order shear deformation model are presented for the static and dynamic analysis of functionally graded plates (FGPs). This theory enforces traction free boundary conditions at plate surfaces. Shear correction factors are not required because a correct representation of transverse shearing strain is given. Unlike any other theory, the number of unknown functions involved is only four, as against ﬁve in case of other shear deformation theories. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Numerical illustrations concern ﬂexural behavior of FG plates with Metal–Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction proﬁles, aspect ratios and length to thickness ratios. Results are veriﬁed with available results in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static and dynamic behavior of functionally graded plates. This paper presents a theoretical investigation in free vibration of simply supported FG beam. Young’s modulus of beam varies in the thickness direction according to power law. Governing equations were found by applying Hamilton’s principle. Navier type solution method was used to obtain frequencies. Diﬀerent higher order shear deformation theories and classical beam theories were used in the analysis. A free vibration frequency is given for diﬀerent material properties.

JVTSD Volume 4, Issue 4

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Feasibility of Controlling Gas Concentration and Temperature Distributions in a Semiconductor Chamber with CT-TDLAS

pp. 297-309 | DOI: 10.5890/JVTSD.2020.12.001

Daisuke Hayashi, Junya Nakai, MasakazuMinami, Takahiro Kamimoto, Yoshihiro Deguchi

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Abstract

The feasibility to control the gas concentration and temperature distributions in a semiconductor process chamber by measuring them was investigated. Gas concentration and temperature distributions for various flow rates were measured with the computed tomography-tunable diode laser absorption spectroscopy (CT-TDLAS). The infrared absorption spectra of multiple laser paths passing through the measured area were collected and the distributions of methane concentration and temperature in the chamber were reconstructed with the computed tomography (CT) calculations. The measured results indicated that the distributions can be independently controlled by measuring with the CT-TDLAS and adjusting the flow rates and the susceptor temperature.

Existence and Exponential Stability for Neutral Impulsive Stochastic Integrodifferential Equations with Fractional Brownian Motion Driven by Poisson Jumps

pp. 311-324 | DOI: 10.5890/JVTSD.2020.12.002

K. Ramkumar, K. Ravikumar, A. Anguraj

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Abstract

In this paper, we establish the results on existence and uniqueness of mild solution of neutral impulsive stochastic integrodifferential equations with fractional Brownian motion driven by Poisson jumps in a Hilbert space. Further, by using an impulsive integral inequality, we study the new sufficient conditions that ensure the exponential stability of mild solution in the mean square moment by utilizing the fractional power of operators and the semigroup theory.

Synchronization and Anti-synchronization for a 4-dimensional Hyperchaotic System

pp. 325-336 | DOI: 10.5890/JVTSD.2020.12.003

Yuansheng Wang, Bo Li, Guiying Lu

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Abstract

Between two 4-dimensional hyper-chaotic systems with unknown parameters, using Lyapunov stability theory, adaptive controller and parameter estimation law are designed to achieve their globally asymptotical synchronization and anti-synchronization. By numerical calculationwith MATLAB, synchronization or anti-synchronization is arrived theoretically but synchronous or anti-synchronous errors of state variables cannot all converge to zero simultaneously during a limited time. The comparative and contrastive studies about system without cubic term indicates that the primary cause is existence of cubic term. It is verified by numerical simulation examples consistently.

Changing Dynamics of the First, Second & Third Approximates of the Exponential Chaotic System & their Synchronization

pp. 337-361 | DOI: 10.5890/JVTSD.2020.12.004

Ayub Khan, Lone Seth Jahanzaib, Pushali Trikha, Taqseer Khan

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Abstract

In this paper, an exponential chaotic system has been studied and its dynamical properties such as phase plots, time series, Lyapunov exponents, bifurcation diagrams, equilibrium points, Poincare sections etc. have been discussed and compared with its first, second and third approximate systems. The aim of this study is to highlight the entirely different dynamics of the approximations of exponential chaotic systems, where many studies simply replace the exponential chaotic system with its first approximation to study it. Also we have synchronized the chaotic systems and its approximations using a novel technique “compound difference synchronization”.

A Passive Vibration Isolator Integrated a Skyhook Damper or a Groundhook Damper

pp. 363-376 | DOI: 10.5890/JVTSD.2020.12.005

Kuinian Li

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Abstract

Presented in this paper is a passive vibration isolator integrated a skyhook damper or groundhook damper. The dynamic behavior of the isolator supporting a lumped mass is investigated using force and displacement transmissibility of the isolator. Force and displacement transmissibility are derived by modelling the new isolator a two-degree-of-freedom system. Numerical simulation and parameter studies of the isolator were performed. It reveals that the new isolator is a passive linear isolator, without any non-linear elements, spring or damper. However, it can bear a large static load and, at the same time, achieve greatly improved vibration isolation without employing high damping element, which is difficult to achieve in practices. Moreover, the implementation of such an isolator in practice is convenient. All these make the isolator attractive for engineering application.

An Analytical Prediction of Periodic Motions in a Discontinuous Dynamical System

pp. 377-388 | DOI: 10.5890/JVTSD.2020.12.006

Siyu Guo, Albert C. J. Luo

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Abstract

Periodic motions in a discontinuous dynamical system are studied. The discontinuous dynamical system consists of three distinct linear dynamical systems with two dierent circular boundaries. Analytical conditions for switching and sliding motions at the two circular boundaries are developed. From such analytical conditions, periodic motions in discontinuous dynamical systems can be determined through specic mapping structures. Illustrations give periodic motions in discontinuous dynamical systems, which are dierent from the continuous dynamical systems. In dierent domains, the motions are dierent, and the discontinuity of the periodic motions at the boundaries is observed, and the sliding motion on the boundaries is also a portion of periodic motion. Such periodic motions in discontinuous dynamical systems do not have any Fourier series. The methodology presented in this paper can be applied to other discontinuous dynamical systems. The circular boundaries can be treated different energy levels as control conditions in engineering systems.

On the Analytical Modeling of a Resonant Fatigue Testing Rig

pp. 389-399 | DOI: 10.5890/JVTSD.2020.12.007

Leilei Chen, Siyuan Xing, Xingzhong Xiong

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Abstract

The drill string is a common rotating structure extensively used in oil exploration and production. The drill string fails under the long-term action of internal and external pressure, axial force, bending stress and torque in the drilling process. In order to facilitate the study of fatigue life of pipe joints, a light-structural and cost-and-time, ecient resonant bending fatigue test scheme is adopted, an analytical resonant bending fatigue test model is established, and the relationship between the parameters such as pipe length and the natural frequency of the sample is explored. The natural frequency and the zero-displacement position of the rst mode of the test sample are predicted. The location of the moving point, the central bending moment and the corresponding normal stress can be used to predict if the test requirements are satised.

JVTSD Volume 5, Issue 1

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Neural Network for Surface-Profile Estimation of Atomic Force Microscope

pp. 1-17 | DOI: 10.5890/JVTSD.2021.03.001

Nyesunthi Apiwattanalunggarn

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Abstract

This paper describes a methodology for implementing an identification algorithm for an atomic force microscope to estimate a surface profile of a sample. A microbeam of the atomic force microscope is modeled as an Euler-Bernoulli beam. A tip-sample interaction force used here is a piecewise function described by the attractive van der Waals force and the repulsive Derjaguin-Muller-Toporov force which can represent the indentation made by a tip of the microbeam into the sample surface. The identification of the instantaneous gap between the tip of the undeformed microbeam and the sample surface is implemented on line based on a trained input-output recurrent network. With the measured cantilevered-beam-tip motion supplied to the recurrent network, the recurrent network is going to compute the estimated gap. The approach being used in this study is in contrast to the conventional approach in that it is based on the signal in the time domain instead of in the frequency domain; therefore, the number of steps involved is fewer. When comparing the proposed approach with the adaptive-tracking controllers based on adaptive control Lyapunov functions, the proposed approach outperforms the adaptive-tracking controllers significantly. Whereas the adaptive-tracking controllers require much more measured signals to supply to the controllers and the parameter estimator. Instead, the proposed approach has to store two units in the tapped-delay-line memory while the identification algorithm is running.

Numerical Analysis of Fluid-Structure Interaction of Fire Doors in Cross-Passages of Subway Tunnels

pp. 19-32 | DOI: 10.5890/JVTSD.2021.03.002

Yong-hang Sun, Zhong Luo, Kai Wei, Yu Wang, Gui-xin Han

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Abstract

This study is concerned with the dynamic response of fire doors in cross-passages of subway tunnels. Fire doors in cross-passages of subway tunnels are prone to failure due to the piston effect. First, a full-size model of a section of tunnel in Shenyang Metro was established. Then, computational fluid dynamics (CFD) was used to simulate unsteady airflow under different train speeds. Pressure on the surface of the fire door was obtained and the pressure was set as the excitation on the finite element model of the fire door. Finally, the structural response of the fire door was obtained through explicit dynamics analysis. Maximum stress on the fire door structure was found to be 10.05 MPa. Consistent results were obtained with the actual failure warping deformation, it can be considered that the piston wind is the main factor leading to the warping deformation of the fire door. The findings provide guidance for the installation and maintenance of fire doors in metro tunnels.

Constructed limit cycles in a discontinuous system with multiple vector fields

pp. 33-51 | DOI: 10.5890/JVTSD.2021.03.003

Siyu Guo, Albert C.J. Luo

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Abstract

In this paper, limit cycles in a discontinuous dynamical system with different vector fields in different domains are constructed. Such limit cycles are obtained through algebraic equations based on specific mapping structures. The stability and bifurcations of limit cycles are studied through eigenvalue analysis. The grazing and sliding bifurcations on the bifurcation trees are presented. Once a grazing or sliding bifurcation occurs, a limit cycle switches to a new limit cycle or vanishes. Such bifurcations (i.e., saddle-node bifurcation, Neimark bifurcation, period-doubling bifurcation, grazing bifurcation, and sliding bifurcation) are for onset and vanishing of limit cycles at specific parameters. This study presents how to construct limit cycles in discontinuous dynamical systems and how to develop the corresponding mathematical conditions of motion switchability at boundaries.

Design and Investigation of the Mini-multilayer Inverse Conical Coil for Micro Displacement Detection in Fuel Injection Nozzles

pp. 53-71 | DOI: 10.5890/JVTSD.2021.03.004

Akin Tatoglu, Claudio Campana, Ying Yu, Hisham Alnajjar, Nikolay Nazaryan

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Abstract

A fuel injector plays an important role in performance and emissions of diesel engines. Among other factors, the quantity of fuel injected into the combustion cylinder is dictated by the nozzle seat and sac geometry, spray hole size and K factor, and the needle lift. These factors can affect the timing of the needle closing, potential bounce and transverse motion of the needle. In order to optimize needle closing, the motion of the needle valve needs to be understood. For this purpose, a mini multilayer conical inductance coil was designed to measure needle valve motion as it is actuated in a nozzle body, with the nozzle being the core of the coil. This approach minimizes intrusion into the injector assembly which can pose a risk for leakage.

Fault identification in T-connection transmission lines based on probabilistic neural network and wave impedance angle

pp. 73-85 | DOI: 10.5890/JVTSD.2021.03.005

Jie Yang, Hao Wu, Qiao-mei Wang, Dong Li, Song-hai Fan

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Abstract

In order to improve the accuracy of internal and external fault identification algorithms for T-connected transmission lines, a new method for fault identification of T-connected transmission line based on the probabilistic neural network and the angle of wave impedance is proposed. Extract the initial voltage and current phasor information of each traveling wave protection unit at a specific frequency based on the S transform, then calculate the included angle of the measured wave impedance at this frequency, and use this to form a T-connection transmission line fault characteristic sample set. The T-connection transmission line fault feature training sample set is input into the probabilistic neural network training and testing to establish a fault recognition model to identify the fault. Simulation results show that the proposed algorithm can accurately identify the internal and external faults of the T-connection transmission line and the specific branch roads outside the zone.

A General Framework for Dynamic Complex Networks

pp. 87-111 | DOI: 10.5890/JVTSD.2021.03.006

Chun-Lin Yang, C. Steve Suh

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Abstract

A general framework applicable for characterizing dynamic complex networks is presented. The framework 1) incorporates a revised Kuramoto model to define constituent dynamics, 2) explores information entropy for the description of global ensemble behaviors, 3) defines the variation of the state of connected constituents using energy, and 4) introduces two new time-dependent parameters, i.e., degrees of coupling, to delineate the extent to which the state of one constituent impacts the other. Information entropy which defines the randomness of constituent energy at the microscopic level provides a definitive measure for the ensemble dynamics at the macroscopic level. Whether a dynamic complex network is evolving toward synchronization or deteriorating and collapsing can be determined by tracking ensemble entropy in time. Two popular topological network structures are examined under the framework for their respective network responses. It is found that, in addition to misrepresenting the true network dynamics, static network structures do not differentiate themselves in resolving network properties such as average path length and degree distribution, thus rendering similar interpretations for the underlying network.

JVTSD Volume 5, Issue 2

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Smoothing Transforms for Dynamical Systems with Non-smooth Input

pp. 113-120 | DOI: 10.5890/JVTSD.2021.06.001

Carmen Chicone, Z. C. Feng

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Abstract

Many control systems incorporate input from actuators. The actuators can be represented as force or displacement input. When an actuator is modeled as a displacement input, there are many prac- tical applications for which the displacement is not smooth and its time derivative, i.e. the velocity, is not continuous everywhere. Nu- merical study for such displacement input becomes tedious since the state variables experience a finite jump at the time of acceleration singularity. Although the acceleration singularity can be avoided if the actuator dynamics is modeled by a force input, such an approach increases the order of the overall system. To preserve the simplicity of the displacement input of the actuators, we propose transforms of state variables so that only the velocity of the displacement in- put appears explicitly in the equations of the dynamical system. In short, we introduce transforms that reduce the order of time deriva- tives of the input. This approach simplifies the numerical solutions for non-smooth displacement input. Moreover, when the transform is applied to a parametrically excited pendulum, the stabilizing effect of the parametric excitation is shown explicitly.

Image Fusion Performance-gains at Different Fusion Levels

pp. 121-130 | DOI: 10.5890/JVTSD.2021.06.002

Xin Zeng, Zhongqiang Luo, Xingzhong Xiong

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Abstract

Image fusion is a branch of multi-source information fusion, which plays an increasingly significant role in the military field. Since the environment is full of many interference factors, including light, dust, etc., the target object cannot be clearly identified. Image fusion based on visible image and infrared image is attractive and promising for the object detection applications. This paper analyzes and compares pixel-level, feature-level and decision-level image fusion, and summa- rizes the performance-gains of image fusion at different levels with ex- amples. It is concluded that pixel-level fusion can be used to process more delicately than feature-level fusion, and the result of feature- level fusion is more delicate than decision-level fusion. Furthermore, we conclude a creative idea, that is pixel-level and feature-level meth- ods can be combined in the future.

Understanding Dynamics of Infinite-Equilibrium Systems via a Quadratic Nonlinear System

pp. 131-147 | DOI: 10.5890/JVTSD.2021.06.003

Siyuan Xing, Albert C.J. Luo, Jianzhe Huang

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Abstract

This paper presented the dynamics of an infinite-equilibrium system based on a quadratic oscillator. Equilibria, stability and singular- ity of such an infinite equilibrium system are discussed through the local analysis, and numerical studies of the periodically perturbed infinite-equilibrium systems are completed. The infinite-equilibrium boundaries in infinite-equilibrium systems can be artificially designed to control motions in the corresponding non-infinite-equilibrium sys- tems. Through this study, one can have a better understanding of dynamics of infinite-equilibrium nonlinear systems. The authors be- lieve infinite-equilibrium systems will have extensive applications in science and engineering.

Generalized Formulation for Free Vibration of Elastic Solids with Static Loads and Application to Rotating Tapered Cantilever Beam Vibration

pp. 149-168 | DOI: 10.5890/JVTSD.2021.06.004

Renfan Luo

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Abstract

By solving the three one-dimensional (1D) nonlinear dynamic dif- ferential equations analytically, it has been proved that unless the nonlinear terms are in first order, a nonlinear dynamic system never has a vibration natural frequency. For an elastic solid with nonlin- ear deformation and with static loads including a rotational angular velocity, a virtual small factor has been introduced to ensure a small deformation, a generalized formulation to predict vibration frequen- cies has been developed. Tapered rotating cantilever beams have been used to validate the formulation against FE analysis, and the analytical and FE results are in a good agreement.

Stability of Higher Order Nonlinear Implicit Fractional Differential Equations by Fixed Point Technique

pp. 169-180 | DOI: 10.5890/JVTSD.2021.06.005

Kausika Chellamuthu

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Abstract

This paper constructs a theoretical framework to analyze stability of higher order nonlinear implicit fractional differential equations. The main theorem asserts the stability and asymptotic stability by making use of Krasnoselskii’s fixed point technique. Results are established in a weighted Banach space to arrive at the compactness requirements directly. Two examples are provided to illustrate the theory.

Reciprocating Compressor Dynamics Modelling by a Bond Graph Approach

pp. 181-194 | DOI: 10.5890/JVTSD.2021.06.006

Enaiyat Ghani Ovy, Qiao Sun

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Abstract

This research is dedicated to developing an analytical physics-based model of a reciprocating compressor based on a bond graph approach. At first, a mathematical model is developed for one-cylinder recipro- cating compressor based on multi-body dynamics, particularly con- sidering planar motion of the rigid bodies using body fixed reference frames. All the dynamical equations of motions are represented and linked altogether by the bond graph that simulates a complete sys- tem model. The model has unique capability to show forces at vari- ous joints, which enhances our understanding of complex system be- havior. Moreover, the consequences of changing coefficients of those forces are accentuated. The utility of the model in fault diagnosis and condition monitoring are emphasized by highlighting the effects of a crack in a joint and a dent on cylinder wall. Nonlinear differen- tial equations extracted from bond graph model are solved efficiently using a MATLAB stiff solver. Responses of the model parts are ana- lyzed later by force analysis along with a comparison with a previous research to examine model validity.

Image Details Enhancement Method via Spectrum Total Variation

pp. 195-205 | DOI: 10.5890/JVTSD.2021.06.007

Liu Chen, Zhi-Shuang Xue, Ming-Ju Chen

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Abstract

In order to enhance the texture details of images and preserve the complete structure of images, we propose a novel image detail en- hancement method based on spectral total variation, which combines the total variation method and spectral analysis method. Firstly, the total variation flow, as a non-ideal high-pass filter, decomposes im- age and obtains the spectral characteristics of different time scales in the transform domain. The transform domain can be regarded as a frequency domain. Then, we construct a special filter in the trans- form domain, and the spectrum features are filtered and enhanced by the filter. Finally, according to the proposed reconstruction method, the filtering results in the transform domain are inversely converted to the spatial domain, that is, the final enhanced image is obtained. The experimental results show that the proposed spectral total varia- tion method can effectively use the spectral information of the image to enhance the local details, so that the enhanced image can obtain more prominent texture information, while maintaining the integrity of the image structure.

JVTSD Volume 5, Issue 3

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On the 100th Anniversary of the Full Member of Russian Academy Of Sciences L.V. Ovsyannikov and the 80th Anniversary of His Follower, Professor N.H. Ibragimov

pp. 207-219 | DOI: 10.5890/JVTSD.2021.09.001

Inna Emelyanova

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Abstract

Two dates coincided in 2019: the centenary of the full member of Russian Academy of Sciences Lev Vasilievich Ovsyannikov (April 22, 1919 { May 23, 2014) and the eightieth anniversary of his follower, professor Nail Hairullovich Ibragimov (January 18, 1939 { November 04, 2018). Through the efforts of them and their numerous students and followers, Sophus Lie's theory of local transformation groups was revived and received promising development.

Louise Petrén – A Mathematician Whose Work Waited for a Century to Be Appreciated

pp. 221-232 | DOI: 10.5890/JVTSD.2021.09.002

Inna S. Emelyanova

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Abstract

Louise Petren (Hedvig Louise Beata Petren-Overton, 1880-1977) was the first Swedish woman to defend her doctoral thesis in mathematics in 1911. It took nearly a hundred years for her thesis to be duly appreciated.

Application of Argument Principle for Study a Structure of Roots of Transcendental Equations

pp. 233-236 | DOI: 10.5890/JVTSD.2021.09.003

Nail Suleiman Khabeev

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Abstract

In study of the structure of shock waves in bubbly liquids we need to find integral curve connecting two singular points of the system of differential equations. We linearized the system of basic equations around equilibrium state. The condition of existence of nontrivial solution of the linear equations leads to the characteristic transcen-dental equation with respect to exponential index. The structure of roots of such equation is studied by using argument principle [1]. It is shown that for compression waves such equation has one real root.

Equation of Rayleigh Noise Reduction Model for Medical Ultrasound Imaging: Symmetry Classiﬁcation, Conservation Laws and Invariant Solutions

pp. 237-247 | DOI: 10.5890/JVTSD.2021.09.004

J. Tanthanuch, E.I. Kaptsov, S.V. Meleshko

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Medical ultrasound imaging provides images of the internal body for diagnosis. Speckle noise is a major problem degrading image quality. In this paper, a wide class of noise reduction models is considered from the group analysis point of view. Group classification is performed, and conservation laws and invariant solutions of the studied equation are presented.

Symmetry Analysis and Reductions Through Conservation Laws of a Generalized Bogoyavlensky-Konopelchenko Equation in (2+1)-Dimensions

pp. 249-257 | DOI: 10.5890/JVTSD.2021.09.005

M.S. Bruzon, M.L. Gandarias

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In this paper we obtain Lie symmetries and travelling wave solutions for a generalized Bogoyavlensky-Konopelchenko equation in (2+1)-dimensions. Moreover, we determine some low-order conservation laws which are invariant under the translation symmetry; consequently they are inherited by the reduced differential equations.

On Preliminary Group Classification of the Isotropic Boltzmann Equation with a Source Term in a Problem of Homogeneous Relaxation by Using Extended Equivalence Group

pp. 259-267 | DOI: 10.5890/JVTSD.2021.09.006

Yu.N. Grigoriev, S.V. Meleshko, A. Suriyawichitseranee

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Abstract

The paper is devoted to preliminary group classification of the spatially homogeneous and isotropic Boltzmann equation with a source term. In fact, the Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. The equivalence transformations considered earlier were extended by the change of time. This extends the set of source functions. The analysis of the extended equivalence group is given. Using optimal systems of finite-dimensional subalgebras of these extended equivalence set of transformations, preliminary classification of the source function is obtained.

Nonlinear Differential Equations Possessing Infinitely many Symmetries: Virasoro Algebra

pp. 269-278 | DOI: 10.5890/JVTSD.2021.09.007

Qing Huang, Renat Zhdanov

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Abstract

The complete classification of inequivalent realizations of the Virasoro algebra by Lie vector fields over the three-dimensional field of real numbers is obtained. Based on this result is our group classification of second-order differential equations admitting infinite-dimensional Virasoro algebras. In particular, we derive all inequivalent secondorder partial differential equations, which admit the direct sum of the Witt algebras. The two well known examples of equations belonging to this class are the wave and hyperbolic Liouville equations. We prove that there is one more nonlinear differential equation enjoying the same group properties as the wave equation.

Some Results About Self-Adjointness of a Class of Nonlinear Wave Equations

pp. 279-283 | DOI: 10.5890/JVTSD.2021.09.008

N.H. Ibragimov, M. Torrisi, R. Tracina

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Abstract

In this paper we show some short notes concerned the nonlinear self-adjointess of a class of wave equations. These results, obtained together with prof. Ibragimov between the end of 2017 and January 2018, were the beginning of a wide study that remained incomplete.

Analytical Dynamics of a Discontinuous Dynamical System with a Hyperbolic Boundary

pp. 285-319 | DOI: 10.5890/JVTSD.2021.09.009

Albert C. J. Luo, Chuanping Liu

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Abstract

In this paper, analytical dynamics of a discontinuous system with a hyperbolic control boundary is studied. The analytical conditions for flow switchability of the discontinuous system are developed from a flow passability theory at boundaries, which are for a better understanding of dynamics of such a discontinuous dynamical system. With the analytical switchability conditions, the sliding and nonsliding motions are described through generic mappings. Periodic motions in the discontinuous dynamical system with hyperbolic boundary are studied through mapping structures. The bifurcation trees of periodic motions are presented, and the corresponding stability and bifurcation of periodic motions are analyzed. The grazing bifurcation for a flow to the boundary is discussed as periodic motion switching. Numerical simulations are completed for illustration of complex periodic motions and flow switchability at the hyperbolic boundary. This paper is dedicated to Nail Ibragimov as a good friend and colleague for 20 years friendship with Albert Luo.

JVTSD Volume 5, Issue 4

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Stability Analysis of a Planetary Gear Train Having Repeated Natural Frequencies

pp. 321-336 | DOI: 10.5890/JVTSD.2021.12.001

M. Javad Abedinilaksar, Jianming Yang

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Abstract

A Planetary gear trains (PGTs) are widely used in numerous engineering fields, such as automotive, aerospace, and wind turbines, etc. In the dynamic model of geared systems, the time-varying meshing stiffness causes parametric resonances or instability. This paper investigates the instability caused by the time changing meshing stiffness in a PGTs with three symmetrically arranged planet gears. Focus is placed on the instability related to the repeated natural frequencies. The multiple scales method is used in the analysis, and the analytical results are verified with numerical simulation based on Floquet theory.

Object Recognition for Remote Sensing Images from UAVs via Convolutional Neural Networks

pp. 337-343 | DOI: 10.5890/JVTSD.2021.12.002

Jiefu Li, Xi Liu, Mingtao Liu, Lijia Cao

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Abstract

In recent years, researches of remote sensing data have begun to develop towards mass information and diversification, and traditional analytical methods alone could not meet the needs of modern data processing. Deep learning methods have developed a lot in the field of computer vision which has provided a new target recognition method for remote sensing images. This paper concentrates on the application of convolutional neural networks(CNN) in object recognition of Unmanned Aerial Vehicle(UAV) remote sensing images: YOLOv3 and Faster R-CNN network model are built on computer and NVIDIA JETSON TX2, and NWPU VHR-10 dataset is used as training and test samples for simulation verification. The results show that the accuracy of remote sensing multiclass target recognition using the YOLOv3 network model is 73.8%, and the detection rate is 0.25s per image on average. The accuracy of using YOLOv3 network model in several network models is second only to Faster RCNN, but its realtime performance is better than one of Faster RCNN. The YOLOv3 network model is more appropriate for carrying on the UAVs.

Modeling of Active Heave Compensation System for Seafloor Drill

pp. 345-357 | DOI: 10.5890/JVTSD.2021.12.003

Yongping Jin, Guangping Liu, Lanxiang Li, Youduo Peng, Buyan Wan

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Aiming at the influences of wave in the process of launch & recovery of the seafloor drill, a velocity sensor is used to gather the data of the heave motion of ship, and a mathematical model of active heave compensation hydraulic serve control system for seafloor drill is established. The simulation of this model based on PID control is performed. The results show that the heave motion compensation control of seafloor drill using PID control makes the tracking accuracy more than 90%. This will improves the reliability and security of the seafloor drill in the process of launch and recovery.

Breathing Crack Detection Using Dynamic Equations and Measurement Data Regression and Filtering Techniques

pp. 359-372 | DOI: 10.5890/JVTSD.2021.12.004

Z.C. Feng, Yi Shang

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Abstract

Structural health monitoring (SHM) traditionally starts from a parametric dynamic model representing damages or defects. The analysis of the dynamic model subjected to vibrational excitations provides the relationship between the response and the damage parameters; this relationship is the basis for determining structural damage from the response measurements. In recent years, data-driven and machine learning methods have been successfully applied to various SHM problems. In this paper, we propose a new method that uses both dynamic equations and measurement data regression and filtering techniques to detect breathing cracks. This method circumvents the dynamic analysis of the system model. We conducted a series of empirical studies based on noisy measurement data and compared the results of several regression and filtering algorithms in our simulations. We found that the proposed method was effective in detecting breathing crack with up to 5% noises in measurements. Among the various data processing algorithms, least squares linear regression following a support vector regression filter on noisy measurement data performed the best.

Bifurcation Trees of (1:2)- Asymmetric Periodic Motions with Corresponding Infinite Homoclinic Orbits in the Lorenz System

pp. 373-406 | DOI: 10.5890/JVTSD.2021.12.005

Siyu Guo, Albert C.J. Luo

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In this paper, bifurcation dynamics and infinite homoclinic orbits of (1:2)- asymmetric periodic motions in the Lorenz systems are studied through the discrete mapping method. The infinite homoclinic orbits pertaining to the unstable periodic motions on the bifurcation trees of (1:2)-asymmetric periodic motions to chaos are determined. The sta- bility and bifurcations of periodic motions are determined through the eigenvalue analysis. A bifurcation tree of (1:2) asymmetric periodic motions, varying with the Rayleigh number, is presented by discrete nodes, and the corresponding harmonic frequency-amplitude characteristics of periodic motions on the bifurcation tree are discussed through finite Fourier series analysis. A sequence of period-doubling bifurcations is observed on the bifurcation tree of the (1:2)- asymmetric periodic motion to chaos. The scenario of (1:2)- asymmetric period-1, period-2, period-4 motions to chaos scenario is illustrated. Homoclinic orbits are as appearance or vanishing of unstable periodic motions on the bifurcation tree. Illustrations of periodic motions and homoclinic orbits are completed for intuitive demonstrations of the corresponding topological structures. This study extends the initial study of the bifurcation tree from the (1:1)-symmetric periodic mo- tions to asymmetric periodic motions then to chaos in the Lorenz system, and the corresponding infinite homoclinic orbits induced by all unstable periodic motions can be determined. Such results can enrich the understanding of bifurcation dynamics of asymmetric periodic motions to chaos in the Lorenz system.

Dynamics of a predator-prey model with Beddington-DeAngelis functional response, omnivory and predator switching

pp. 407-428 | DOI: 10.5890/JVTSD.2021.12.006

Prabir Panja

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Abstract

In this paper, a predator-prey model has been developed by considering Beddington-DeAngelis functional response among the interaction of three species prey, middle predator and top predator. It is assumed that middle predator consumes only prey, but top predator consumes prey as well as middle predator. The concept of omnivory has been introduced in this model. Also, it is assumed that due to omnivory property, the top predator has a chance to prefer the food (prey) to consume. Here two types of predator switching behavior such as preferential switching and density dependent switching have been introduced. Diﬀerent possible equilibrium points are evaluated and the stability of the system has been investigated around these points. Theoretical analysis of for the existence condition of Hopf bifurcation of the system has been studied with respect to $w_4$. It is found that the increase of death rate of middle and top predator may be responsible for the extinction of both the species or that particular species. It is observed that omnivory may lead the system towards stability. It is also observed that the predator switching behaviour may strengthen the stability and persistence of all populations. Finally, some numerical simulation results have been presented to validate the analytical ﬁndings.

JVTSD Volume 6, Issue 1

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Existence and Uniqueness of Solutions for the Neutral Fractional Integro-Differential Equations with Fractional Integral Boundary Conditions

pp. 1-11 | DOI: 10.5890/JVTSD.2022.03.001

Ahmed A. Hamoud, Abdulrahman A. Sharif, Kirtiwant P. Ghadle

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In this paper, we establish sufficient conditions for the existence and uniqueness of solutions for a class of boundary value problems with integral condition for neutral fractional integro-differential equations. The results are established by the application of the contraction mapping principle, Leray-Schauder alternative theorem and Krasnoselskii fixed point theorem. An example is provided to illustrate the main results.

The liquor quality recognition using magnetic resonance spectrum based on Kernel principal component analysis and convolutional neural network

pp. 13-20 | DOI: 10.5890/JVTSD.2022.03.002

Lin-Lin Cheng, Lei-Lei Chen, Qiao-Mei Wang, Ming-Ju Chen, Xing-Zhong Xiong

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In order to effectively recognize and identify liquor quality by nuclear magnetic resonance (NMR) spectrum data, we propose a hybrid data processing and recognition algorithm. In this algorithm Kernel principal component analysis (KPCA) was used to remove the correlation and reduce dimension of the NMR spectrum, and then convolutional neural network (CNN) was used for classification and identification of the processed spectrum. The compared experiment result show that the proposed KPCA+CNN method can obtain higher accuracy than CNN and PCA+CNN methods based on the NMR spectrum. The KPCA+CNN algorithm has good application prospect and reference value.

Underactuated Mechanical Systems – A Review of Control Design

pp. 21-51 | DOI: 10.5890/JVTSD.2022.03.003

Zilong Zhang, C. Steve Suh

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Abstract

An active research subject in robotics and aeronautics, underactuated mechanical systems (UMS) have been extensively explored for applications where maintaining stability and safety is of paramount importance. All contemporary control methodologies of recent have been applied to controlling various UMS designs. A great amount of effort is documented on a yearly basis by journals and conference proceedings claiming to offer effectively better solutions to improved UMS control. However, control design for UMS is still considered an open problem due to issues including parametric uncertainty, coupled nonlinear dynamics, and need for fewer control actuators. This presentation presents a comprehensive survey on the present state-of-affairs pertaining to the control of UMS of different configurations. Relevant references in the open literature dating as far back as 1990 are reviewed and meticulously categorized. Popular underactuated control techniques are reviewed, and their primary features re-examined, for their strengths and where they fall short in addressing properties of underactuation including coupled dynamics, nonlinearity and nonstationarity. No prior review articles have provided similarly critical while also in-depth review of published works on UMS control. This survey serves as an expanded reference for researchers and practitioners who seek to control UMS with efficacy.

Damping analysis of power system stabilizer based on transient equivalent circuit

pp. 53-61 | DOI: 10.5890/JVTSD.2022.03.004

Xiao-lin Su, Yi-qiang Yang, Wen-rui Bai, Cheng Chen

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Abstract

A damping analysis method for power system stabilizer (PSS) based on transient circuit is proposed. The transient equivalent circuit of sixth order generator model and its energy function is obtained According to circuit theory, the damping of excitation system is analyzed. Based on the analysis, a PSS damping evaluation method is proposed. The simulation results of a single machine infinite bus system show that the proposed method can accurately evaluate the damping of PSS.

A Theory for Singularity and Stability in Two-dimensional Linear Systems

pp. 63-105 | DOI: 10.5890/JVTSD.2022.03.005

Albert C. J. Luo

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Abstract

In this paper, two-dimensional dynamical systems with constant and linear vector fields are presented. Dynamical systems with one-variable vector fields are presented and the singular dynamics of two-dimensional linear systems was discussed. Based on the variable-inde- pendent and variable-crossing linear vector fields, the dynamics based on saddle, sink, source and center equilibriums are discussed. Two-dimensional linear dynamical systems with two linear vector fields are discussed, and local dynamics of the saddle and focus equilibriums are presented. The dynamics and stability of two-dimensional linear dynamical systems are presented comprehensively for a better understanding of dynamical behaviors of the two-dimensional linear systems.

JVTSD Volume 6, Issue 2

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Singularity and 1-dimensional Flows in 2-D Single-variable Quadratic Systems

pp. 107-194 | DOI: 10.5890/JVTSD.2022.06.001

Albert C. J. Luo

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Abstract

In this paper, two-dimensional nonlinear systems possessing univariate quadratic vector fields with a single-variable only are discussed, and the appearing and switching bifurcations for the 1-dimensional flows (e.g., sink and source flows, and up-parabola and down-parabola flows) will be discussed herein. The upper-saddle and lower-saddle flows are for the appearing bifurcations of the sink and source flows. The increasing-inflection and deceasing-inflection flows are for the appearing bifurcations of the up-parabola and down-parabola flows. The infinite-equilibriums are for switching bifurcations between the sink and source flows and the up-parabola and down-parabola flows. The bifurcations of the 1-dimensional flows are much richer than the bifurcations of equilibriums. The switching of the sink and source flows with parabola flows are very significant in applications, and it can be used to determine flow singularity.

The Non-Classical Problem of Thermoelastic Stability of an Elastically Restrained Orthotropic Plate of Variable Thickness

pp. 195-206 | DOI: 10.5890/JVTSD.2022.06.002

Razmik M. Kirakosyan, Seyran P. Stepanyan

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In this paper elastically clamping conditions are given for the bending problem of rectangular plate. It is assumed that these conditions and physical and mechanical properties of the plate material do not depend on temperature. Within the framework of the momentless theory, expressions are obtained for compressive forces, arising as a result of a uniform increase in temperature. A wide range of elastic pinching conditions is considered. In the general case, both a system of differential equations of partial derivatives with unknown variable coefficients and corresponding boundary conditions are obtained to solve the addressed problem. Unknown functions are represented by multiples. A homogeneous system of algebraic equations with respect to unknown coefficients of polynomials is obtained. For certain problems, introducing dimensionless quantities, a technique to calculate the critical temperature by the collocation method is described.

Mechanisms with Negative Stiffnesses for Simplified Designs of Broad Band Passive Vibration Isolation

pp. 207-214 | DOI: 10.5890/JVTSD.2022.06.003

Z.C. Feng

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Abstract

Structures with nonlinear stiffnesses have been proposed for passive vibration isolation to achieve high static stiffness and low dynamic stiffness. Unfortunately, the design of nonlinear structures is very cumbersome because of the nonlinear geometry. Mechanisms with negative stiffnesses have found successful applications in industry. These mechanisms could be included in mechanical vibration courses since the design requires only the linear analysis. However, the stiffnesses of these structures with a compressive load are not available in the literature. This paper provides derivation of the stiffnesses of beam mechanisms with compressive loads. The derivation is based on the solution of the ordinary differential equation in the buckling analysis of columns.

A New Method of Fault Phase Selection for Transmission Line Based on Composite Feature of Fault Current and Support Vector Machine

pp. 215-234 | DOI: 10.5890/JVTSD.2022.06.004

Jie Yang, HaoWu, Sheng Wang, Xing-xing Dong

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Abstract

Aiming at the problem of fault phase selection for high-voltage transmission lines, a new method for identifying fault types of transmission lines based on the composite characteristics of fault current combined with support vector machines (SVM) is proposed. First, perform phase-to-mode conversion on the three-phase currents fault component extracted by the measurement unit, and then obtain the Euclidean distance, cosine similarity and Pearson correlation coefficient between the two modulus currents, and finally combine the calculated results in order. Characteristic sample vector to characterize the type of transmission line fault. Then use the powerful pattern recognition capability of the support vector machine to identify the fault type. The simulation results show that the proposed algorithm can accurately identify specific fault types of transmission lines under various working conditions.

Correlation between No-slip and Slip Boundary Conditions Associated with a Two-dimensional Navier-Stokes Flows in a Plane Diffuser

pp. 235-246 | DOI: 10.5890/JVTSD.2022.06.005

Ranis Ibragimov, Vesselin Vatchev

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Abstract

We examine the viscous effects of slip boundary conditions for the model describing two-dimensional Navier-Stokes flows in a plane diffuser. It is shown that the velocity profile is related to a half period shifted Weierstrass function with two parameters. This allows to approximate the explicit solution by a Taylor series expansion with two new micro-parameters, that can be measured in physical experiments. It is shown that the assumption for no-slip boundary conditions is stable in the sense that a small perturbation of the boundary values result in a small perturbation in the solutions.

JVTSD Volume 6, Issue 3

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Onset of Oscillations Driven by Temperature Gradients in Oscillatory Heat Pipes

pp. 247-271 | DOI: 10.5890/JVTSD.2022.09.001

Carmen Chicone, Z.C. Feng, Stephen J. Lombardo, David G. Retzloff

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Abstract

Dynamic evaporation and condensation processes contribute to successful operating regimes in oscillating heat pipes (OHPs), but they can also be responsible for evolution to a stagnant state where all liquid slugs are in the cold zone of the OHP system. In fact, accumulation of liquid slugs in the cold zone is considered to be the main cause for the slow startup of OHP systems. We formulate a model for the dynamics of liquid slugs and vapor plugs, which takes into account the effects of evaporation and vapor compressibility, and use it to examine mechanisms that drive the system from stagnation to oscillation. For example, modeled states where all menisci are located in the boundary between the hot and cold zones are equilibria in the presence of an imposed temperature gradient. Linear stability analysis at such equilibrium states corresponding to the stagnant case, i.e., all liquid slugs in the cold zone, is used to show that stagnant states bifurcate to self-excited oscillations when the system is subjected to sufficiently high temperature gradients. Our results extend those for an earlier model for one slug in a pipe closed at one end to a multi-slug model with pipe geometry characteristic of operational OHPs.

Dynamical Analysis of a Fractional Order two Species Model of Pest and its Predator

pp. 273-296 | DOI: 10.5890/JVTSD.2022.09.002

Prabir Panja

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Abstract

This paper considers a fractional order two species model incorporating pest and its predator population. It is assumed that the pest population is infected by a disease. Due to this infection, pest population is classified into two sub populations such as susceptible pest and infected pest population. For the biological control of pest species, the predator of pest population is introduced. Here, it is assumed that predator consumes susceptible as well as infected pests. The uniqueness, non-negativity and boundedness of the solutions of the fractional order system have been studied. Locally asymptotic stability of the equilibrium points has been investigated. Also, global stability of the interior equilibrium point has been analyzed. The existence condition of Hopf bifurcation in the proposed model has been studied. It is found that the stability of the model increases as the value of fractional order derivative $\alpha$ gradually decreases.

Bifurcations and Harmonic Responses of Period-1 Motions in a Periodically Excited Spring Pendulum

pp. 297-315 | DOI: 10.5890/JVTSD.2022.09.003

Yu Guo

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In this paper, the complete bifurcation trees of period-1 motions to chaos are predicted through discrete implicit maps for a periodically excited spring pendulum. Such discrete maps are used to construct mapping structures that describe any periodic motions in the system. Analytical bifurcation trees are obtained through the nonlinear algebraic equations of such implicit maps. The corresponding stability and bifurcations are achieved through eigenvalue analysis. For a better understanding of the motion complexity, the corresponding frequency-amplitude characteristics are presented through harmonic responses. Finally, simulation results of periodic motions are illustrated in compare to the analytical predictions.

Strange Non-Chaotic Attractors with Unpredictable Trajectories

pp. 317-327 | DOI: 10.5890/JVTSD.2022.09.004

Marat Akhmet, Mehmet Onur Fen, Astrit Tola

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Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized to show the presence of unpredictability.

Numerical and Electrical Simulation of a Hindmarsh-Rose Neuron Model

pp. 329-341 | DOI: 10.5890/JVTSD.2022.09.005

Yan Liu, He Zhang, Yiming He

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Abstract

In order to simulate and study the firing activities of a biological neural model, different technologies have been developed in the field of neural morphology. In this paper, a Hindmarsh-Rose(HR) neuron model is analyzed numerically by a middle point integration method to unfold the complex bifurcation structures. The corresponding analog circuit is designed to reproduce the firing phenomenons according to the HR neuron model. The implementation of the circuit indicates that the circuit model reproduces several neuronal behaviors similar to the numerical model. These results can be used both to design a circuit implementation of the HR neuron model mimicking the diversity of neural response and as guidelines to achieve higher speed and lower hardware cost in large-scale implementation of the biological neural networks.

JVTSD Volume 6, Issue 4

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Impacting Chatter and Stuck Dynamics of a Constrained Cantilever Beam

pp. 343-360 | DOI: 10.5890/JVTSD.2022.12.001

Albert C. J. Luo, Richard George

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In this paper, the forced vibration of a cantilever beam at the free end constrained by two stops is studied. During vibration, the cantilever beam will impact and stuck with the two stops at the free end. Thus, the beam vibration will have different boundary conditions. It should be considered how many modes of vibrations can be used to describe the beam vibration. For impacting chatter and stuck at the free end of the beam, the constrained cantilever beam vibration is discussed in this paper, and analytical conditions for motion switching at the boundary of the cantilever beam are presented. From the analytical conditions, numerical simulations of periodic motions with motion switching are given for illustrations.

Detecting Smoking Behaviors in Public Places Based on T-Yolov4-tiny

pp. 361-371 | DOI: 10.5890/JVTSD.2022.12.002

Ke-Yuan Tang, Chuan-Li Liu, Le-Cai Cai, Kui Cheng, Xing Liu, Shao-Song Duan

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Abstract

Smoking or passive smoking is not only harmful to health, but also easy to cause fires. However, there has been a lack of effective supervision of smoking behavior in public places. Most of the existing supervision methods rely on on-site patrols by supervisors, video surveillance or smoke alarms. These methods have problems such as low efficiency and low accuracy. In order to solve the problems, this paper proposes the T-Yolov4-tiny detection algorithm based on the Yolo lightweight network Yolov4-tiny. Specifically, multiple convolution layers are added to the original network to improve the CSPBlock Network structure; the 1$\mathrm{\times}$1 convolutional layers are used to reduce the amount of network calculations; the scale of the input image is increased to improve the ability of small target detection; the K-means clustering algorithm is utilized to optimize the anchor box size considering the actual target size in the data set, in order to improve the accuracy of the model. Then, a smoking behavior data set (named as Smoking-YBU) was collected by both web crawlers and manual collection. The experimental results show that, compared with the Yolov4-tiny algorithm, the mean average precision (mAP) of the T-Yolov4-tiny algorithm proposed in this paper increases by 12.69\% on the Smoking-YBU, and the detection speed can also meet real-time requirements.

Analytical and Experimental Analysis of Periodic Oscillations in a Nonlinear Temperature Control System

pp. 373-385 | DOI: 10.5890/JVTSD.2022.12.003

Bo Yu

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Abstract

This research studies the periodic temperature oscillations of a temperature control system. The nonlinear differential equation of a micro-controller-based temperature control system is derived using the energy balance method. The system parameters are optimized based on the experimental data. The method of implicit mapping is introduced. Through this mapping structures of periodic temperature responses, the analytical solutions of the steady-state temperature oscillations are computed which can be used to predict the experimental response. From the results of the implicit mapping, the amplitude curves of the Fourier series are calculated. Finally, the comparisons of the numerical, analytical, and experimental results are presented.

Nonlinear Evolution and Persistence of Cellular Patterns in Self-Sustained Two-Dimensional Detonations

pp. 387-411 | DOI: 10.5890/JVTSD.2022.12.004

S. Roy Choudhury, Hardeo M. Chin, Sheikh Salauddin, Kareem A. Ahmed

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Abstract

A nonlinear theory for the development and persistence of cellular two-dimensional patterns behind the shock front in self-sustained detonations is developed. A recent, significantly simplified and carefully-validated, detonation model is used as the basis for the analysis.In the spirit of earlier investigations of a variety of hydrodynamic and hydromagnetic instabilities, crossed-field microwave sources, tokamak edge plasmas, and other areas, our first approach here replaces the actual numerically computed equilibrium profiles by box-shaped ones having a jump discontinuity. The results for both the shapes and dimensions of the persistent two-dimensional cells picked out by our nonlinear analysis agree well with those in earlier simulations for the same sets of parameters. Our theory goes further, allowing predictions of non-trivial regions in the multiparameter space where persistent two-dimensional cells are possible. The only significant discrepancy from numerical results is in the wavelength of the cellular patterns along the reaction channel.Approximations of actual equilibrium profiles by step discontinuities, as done here, are most accurate for long-wavelength regimes where the waves essentially do not register the actual spatial profiles. Future work towards remedying the above discrepancy will be based on generalized normal forms in the spirit of what is usually referred to as 'collective coordinate' analysis, involving coefficients which are integrals over the spatially inhomogeneous equilibrium profiles.

Modeling and Control of the Locomotion of a Monopod Robot Mounted to a Vertical Slider

pp. 413-430 | DOI: 10.5890/JVTSD.2022.12.005

Siyuan Xing, Bradley Y.N. Kwan, Pengji Duan

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Abstract

This paper studies the locomotion of a monopod robot mounted to a vertical slider. The robot is driven by two electric motors attached to its hip. Although the system is often used to develop and test low-level controllers of legged robots, its dynamics was only studied from the lumped model with massless legs. The actual system is more complex and interesting because it is over-actuated and single-degree-of-freedom during the stance phase but under-actuated and three-degree-of-freedom during the flight phase. In this paper, the equations of motion of the legged robot during stance and flight phases are established through the Euler-Lagrange method. The switching law governing phase transitions is derived based on the assumption of conversation of angular momentum. A phase-switching controller is proposed to stabilize dynamic gaits of the robot. Numerical simulations of the robot's locomotion with/without control are carried out through a Stateflow model. Results are validated through numerical simulations powered by Simscape Multibody. The effect of mass distribution of the hip and legs on jump height is discussed for optimized deign.

JVTSD Volume 7, Issue 1

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Analytical and Numerical Methods in Differential Equations for the 100th Birthday Anniversary of Nikolai N. Yanenko

pp. 1-3 | DOI: 10.5890/JVTSD.2023.03.001

S. V. Meleshko, S. Moyo, E. Schulz, J. Tanthanuch

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Abstract

This special topic section collects recent developments on methods in differential equations dedicated to Nikolai Yanenko’s 100th birthday anniversary. The papers were presented at the International Con- ference ‘Analytical and Numerical Methods in Differential Equations (Yanenko 100)’ which was held during 23-27 August 2021. This con- ference was a celebration of Yanenko’s foundational contributions on analytical and numerical methods in differential equations. Its top- ics ranged from physical experiment and mathematical modelling of real problems all the way to abstract mathematical objects. The 6 papers published herein were selected from the 76 presentations to share these advanced developments in differential equations with the community of Journal of Vibration Testing and System Dynamics.

Branching Rules and Subduced Representations Applied to Lie Point Symmetries of Differential Equations

pp. 5-13 | DOI: 10.5890/JVTSD.2023.03.002

R. Campoamor-Stursberg

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Abstract

Vector field realizations of Lie algebras in connection with the representation theory and the branching rule problem associated to embeddings of semisimple Lie algebras are considered. This allows to determine if a subalgebra in a given realization corresponds to an irreducible embedding, as well as to determine multiplicities in the branching rules. The invariants of the realizations associated to such embeddings are used to construct (second-order) systems of ordinary differential equations possessing a fixed Lie algebra of point symmetries. It is shown that for any embedding $\mathfrak{g}^{\prime}\subset\mathfrak{g}$ and any faithful representation there exists an integer $k$ such that for any $n\geq k$, systems of order $n$ with exact Lie point symmetry $\mathfrak{g}^{\prime}$ can be constructed.

Mixed variational problem for a generalized Darcy–Forchheimer model driven by hydraulic fracture

pp. 15-21 | DOI: 10.5890/JVTSD.2023.03.003

Victor A. Kovtunenko

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Abstract

The model of a stationary flow in porous media stemming from hydraulic fracking and accounting for inertial phenomena is considered. The incompressible fluid is modeled by a nonlinear Darcy--Forchheimer (DF) equation under mixed boundary conditions, which are appropriate for a fluid-driven fracture. The classical DF equation is generalized with respect to a growth exponent $m$ and inhomogeneous coefficients. Using mixed variational formulation of the problem for unknown fluid velocity and fluid pressure, the well-posedness theorem is proved for arbitrary $m>1$. The developed Lagrange multiplier formalism is advantageous for optimal shape design of fractures.

Higher Order First Integrals of Autonomous Dynamical Systems in Terms of Geometric Symmetries

pp. 23-30 | DOI: 10.5890/JVTSD.2023.03.004

Antonios Mitsopoulos, Michael Tsamparlis

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Abstract

In general, a system of differential equations is integrable if there exist `sufficiently many' first integrals (FIs) so that its solution can be found by means of quadratures. Therefore, the determination of the FIs is an important issue in order to establish the integrability of a dynamical system. In this work, we consider holonomic autonomous dynamical systems defined by equations $\ddot{q}^{a}= -\Gamma_{bc}^{a}(q) \dot{q}^{b}\dot{q}^{c} -Q^{a}(q)$ where $\Gamma^{a}_{bc}(q)$ are the coefficients of a symmetric (possibly non-metrical) connection and $-Q^{a}(q)$ are the generalized forces. We prove a theorem which produces the FIs of any order of such systems in terms of the `symmetries' of the geometry defined by the quantities $\Gamma_{bc}^{a}(q)$. We apply the theorem to compute quadratic and cubic FIs of various dynamical systems.

Symbolic Methods for Estimating the Sets of Solutions of Ordinary Differential Equations with Perturbations on a Finite Time Interval

pp. 31-37 | DOI: 10.5890/JVTSD.2023.03.005

A. N. Rogalev

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Abstract

In many papers and reports of academician N.N. Yanenko, problem statements are presented that require computing the accuracy of numerical results, depending on perturbations. Such problems are equivalent to problems of stability research. The problems of motion stability over a finite time interval are of considerable interest. This is also due to the fact that most of the methods for studying stability determine stability as $t \to \infty $. Practical stability over a finite time interval means that the solutions are uniformly bounded with respect to the set of initial values and the totality of disturbing influences.

On the Derivation of the Equations of Gravitation and Electrodynamics From the Generalized Least Action Principle and the Nonrelativistic Models of the Universe

pp. 39-47 | DOI: 10.5890/JVTSD.2023.03.006

V. V. Vedenyapin, N.N. Fimin, A.A. Russkov, M.Yu. Voronina

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Abstract

Of the Maxwell and Einstein equations in the framework of the Vlasov--Maxwell--Einstein equations from the classical, but more general principle of least action. The resulting derivation of the Vlasov--type equations gives the Vlasov--Einstein equations different from those proposed earlier. A method is proposed for the transition from kinetic equations to hydrodynamic--type equations. In the case of Hamiltonian mechanics, the transition to the Hamilton--Jacobi equation from the hydrodynamic consequences of the Liouville equation is possible, as was done already in quantum mechanics. Thus, in the nonrelativistic case, we obtain the Milne--McCrea{--type} solutions.

Methods for Constructing Reciprocal Transformations

pp. 49-58 | DOI: 10.5890/JVTSD.2023.03.007

P. Siriwat, S. V. Meleshko

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Abstract

A new method for constructing reciprocal transformations is proposed. The method uses the same steps as for finding equivalence group of transformations. It provides a systematic tool for finding classes of reciprocal transformations. As an illustration the method is applied to the one-dimensional gas dynamics equations, and new reciprocal transformations are found.

Bifurcations and Saddle-Sink-Source Networks in Variable-Independent Quadratic Systems

pp. 59-112 | DOI: 10.5890/JVTSD.2023.03.008

Albert C. J. Luo

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This paper presents a theory for nonlinear dynamics of dynamical systems possessing variable-independent univariate quadratic vector fields. The dynamical systems with a constant vector field and a variable-independent quadratic vector field are presented first, and the 1-dimensional flows discussed. Dynamical systems with linear and quadratic variable-independent univariate vector fields are discussed, and the corresponding bifurcation and global dynamics are discussed. Dynamical systems with two variable-independent univariate quadratic vector fields are analyzed, and the corresponding bifurcations and global dynamics are discussed through the first integral manifolds.

JVTSD Volume 7, Issue 2

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Mapping the Russian Internet Troll Network on Twitter using a Predictive Model

pp. 113-128 | DOI: 10.5890/JVTSD.2023.06.001

Sachith Dassanayaka, Ori Swed, Dimitri Volchenkov

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Abstract

Russian Internet Trolls use fake personas to spread disinformation through multiple social media streams. Given the increased frequency of this threat across social media platforms, understanding those operations is paramount in combating their influence. Building on existing scholarship on the inner functions within influence networks on social media, we suggest a new approach to map those types of operations. Using Twitter content identified as part of the Russian influence network, we created a predictive model to map the network operations. We classify accounts type based on their authenticity function for a sub-sample of accounts by introducing logical categories and training a predictive model to identify similar behavior patterns across the network. Our model attains 88\% prediction accuracy for the test set. Validation is done by comparing the similarities with the 3 million Russian troll tweets dataset. The result indicates a 90.7\% similarity between the two datasets. Furthermore, we compare our model predictions' on a Russian tweets dataset, and the results state that there is 90.5\% correspondence between the predictions and the actual categories. The prediction and validation results suggest that our predictive model can assist with mapping the actors in such networks.

Spinning of oscillating internal gravity waves from a group theoretical standpoint

pp. 129-140 | DOI: 10.5890/JVTSD.2023.06.002

Nail Ibragimoiv, Ranis N. Ibragimov

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Abstract

A new class of exact solutions of the non-linear two-dimensional Boussinesq model for internal gravity waves is derived in this paper. The most general forms of invariant solutions, which can not be guessed from the anisotropic property and correspondingly were not reported in previous studies, are presented in this paper by infinite-dimensional Lie algebra spanned by the infinitesimal symmetries. As a particular example, it is shown here that the nonlinear two-dimensional boussinesq model for internal gravity waves is invariant with respect to the dilations and rotation symmetries that provide the class of exact solutions that has not been reported in previous studies. The new remarkable property of spinning phenomena is observed for internal waves, which has not been reported in the previous studies. The effect of nonlinearity and the earth rotation on the spinining phenomena has been studied both numerically and analytically.

Statics analysis and strength optimization of squirrel cage elastic support structure

pp. 141-152 | DOI: 10.5890/JVTSD.2023.06.003

Jia-xi Liu, Zhong Luo, Lei Li, Kai-ning Liu

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Abstract

The critical speed of aeroengine can be adjusted by designing the support stiffness of elastic support structure. Squirrel cage elastic support structure is a common elastic support structure, so it is very important to optimize its design steps and calculate its stiffness accurately. The static characteristics of the squirrel cage elastic support structure such as stiffness and strength characteristics are analyzed, and the stiffness value, deformation and stress clouds of the structure are obtained, which are based on the finite element method. Then, the static stiffness test platform of the squirrel cage elastic support structure is built to verify the validity of the experiment from the perspective of simulation. Experimental verification shows that the experimental test values have good agreement with the simulation values, which proves the correctness of the simulation results. Finally, in order to achieve the maximum strength of the structure under the condition of specified installation space and specified stiffness value. The genetic algorithm is used to optimize the structure. The rule of the optimization result is summarized, which is verified by the theoretical analysis and simulation.

Performance Comparison of Cooperative Spectrum Sensing Models Based on Machine Learning

pp. 153-167 | DOI: 10.5890/JVTSD.2023.06.004

Qian Hu, Zhong-Qiang Luo, Wen-Shi Xiao, Cheng-Jie Li

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Abstract

So far machine learning (ML) has become increasingly significant in spectrum sensing (SS) for future intelligent wireless communications. In order to obtain an effective SS performance in fading channel, this paper proposes a GMM (Gaussian Mixture Model) based cooperative SS under the conditions of AWGN (Additive White Gaussian Noise) channel and Rayleigh flat fading channel. For evaluating the SS performance, numerous NB (Naive Bayes) and SVM (Support Vector Machine), MLP (Multi-Layer Perceptron) based ML method, as well as the traditional cooperative SS technologies (AND criterion, OR criterion, and Maximum Ration Combining (MRC)) are also investigated for performance comparison. The ROC (receiver operating characteristics) and AUC (area under the curve) performance index is used to compare performance. Simulation results and analysis show that the proposed GMM-based cooperative SS enable acquire the best performance under the Rayleigh channel.

Impulse response of an elastic rod with a mass-damper-spring termination

pp. 169-186 | DOI: 10.5890/JVTSD.2023.06.005

Siyuan Xing, Jian-Qiao Sun

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Abstract

This paper investigates the impulse response of a longitudinally vibrating rod with a mass-damper-spring termination. The equations of motion of the system are derived using Lagrange's method. The vibration of the rod consists of rigid-body and elastic motions. The impulse response is predicted with a particular solution method which constructs the response as the summation of the solution satisfying homogeneous boundary conditions and a particular solution dealing with non-homogeneous boundary conditions. The particular solution method transforms the original partial differential equation to discrete dynamic systems represented in a state-space form. The transient and total impulse responses at selected locations on the rod are studied in detail. The vibration reduction of the rod by tuning the mass-damper-spring system is discussed with the help of root locus with respect to the mass, damping and stiffness parameters. The tuning of the mass-damper-spring system can change coupling between the rigid-body and elastic motions, which in turn can significantly affect the response of the rod. The method of particular solution is validated through the error analysis and response comparison of a rod with free-free boundary conditions.

Bifurcations and Saddle-Limit Cycle Networks in Crossing-Variable Quadratic Systems

pp. 187-252 | DOI: 10.5890/JVTSD.2023.06.006

Albert C. J. Luo

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Abstract

This paper presents a theory for nonlinear dynamics of dynamical systems with two variable-crossing univariate vector fields. Dynamical systems with a variable-crossing univariate linear and quadratic vector fields are discussed, and the corresponding bifurcation and global dynamics are presented. The saddle-center bifurcations are presented through parabola-saddle bifurcations. Dynamical systems with two crossing-variable univariate quadratic vector fields are discussed, and the switching and appearing bifurcations for saddles and centers are discussed through the first integral manifolds, and the homoclinic networks will be first presented. Double-inflection bifurcations are for appearance of the saddle-center network, and the homoclinic networks with centers are constructed. The saddle-center networks with limit cycles are presented from the first integral manifolds.

JVTSD Volume 7, Issue 3

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Global Sensitivity and Stability Analysis of a Parametrically Excited Energy Harvesting System

pp. 253-263 | DOI: 10.5890/JVTSD.2023.09.001

Luiz Oreste Cauz, Fabio Roberto Chavarette, Estevao Fuzaro de Almeida

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Abstract

Energy harvesting is the process of capturing and transforming ambient energy into a useable form. Solar energy, thermal gradients, acoustical and mechanical vibrations are all examples of energy harvesting sources. Vibration Energy Harversting Systems (VEHS) are systems that employ vibrations as a source. VEHS-based energy harvesters are known as a supplementary power source, which provide small amounts of energy for slow-load applications or to charge and operate remote devices and sensors whose require small amounts of energy to operate, such as hearing aids, pacemakers, spinal cord stimulators, and microelectromechanical systems. The objective of this work is to analyze the stability of a parametrically excited energy harvesting system that uses piezoelectric materials as a transducer. The objective is to optimize the energy produced by analyzing the system's behavior while the physical parameter values are changed. In this regard, it is essential to do a preliminary global sensitivity analysis of the physical parameters in order to determine which parameters, when altered, influence more to energy production. The Sobol' indices are used to do the sensitivity analysis. The stability analysis is then performed using the results of Floquet's Theory and the state transition matrix approximation techniques developed by Sinha and Butcher. Sinha and Butcher's technique, based on Picard iterations and Chebyshev polynomial expansions, aims to find approximate solutions for periodic systems in time. An essential characteristic that is well documented in the literature is that vibrational energy harvesting systems have efficient responses when the physical parameters of the system are set so that the system operates in resonance with the parametric excitation source. As a result, when the system is in resonance with the external excitation source, significant system stability outcomes are obtained.

Quasiperiodic energy harvesting in a delayed Rayleigh-Duffing oscillator near the 3-subharmonic resonance

pp. 265-273 | DOI: 10.5890/JVTSD.2023.09.002

Ilham Kirrou, Amine Bichri, Mohamed Belhaq

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Abstract

The paper studies quasiperiodic vibration-based energy harvesting in a forced and delayed Rayleigh-Duffing oscillator coupled to a piezoelectric circuit. The study focuses on the effect of the time delay on the output power performance near the subharmonic resonance of order 3. Using the multiple scales method, quasiperiodic solutions and the corresponding output powers are obtained near the subharmonic resonance. The effect of the delay parameters on the energy extraction performance is analyzed in the case where the delay is introduced either in the position, in the velocity or in both. The analytical results supported by numerical simulations showed the potential of the time delay to achieve hight quasiperiodic output power over a large bandwidth around the 3-subharmonic resonance region.

Energy Transmission and Energy Harvesting via an Electro-dynamical Transducer

pp. 275-284 | DOI: 10.5890/JVTSD.2023.09.003

Evgeniy D. Pechuk, Tatyana S. Krasnopolskaya

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Abstract

This paper addresses energy transmission via an electro-dynamical transducer from the amplifier and energy harvesting from wave field. In the first case an amplifier is considered as a self-exciting system with a limited power. Electrical current produced by it is converted by the transducer into mechanical force, which leads to vibrations of the base. A mechanical oscillator is mounted on the transducer base. The influence of oscillator vibrations on the formation of the driving force leads to the Sommerfeld --Kononenko effect. Expressions for supplied and consumed powers are shown. The energy harvesting problem is also discussed. The classical results for wave power harvesting by wave energy extractor as a single degree of freedom system are presented in the second considered problem. The example includes an axisymmetric buoy which oscillates and is subjected to its natural hydrostatic restoring force. Main attention is focuses on the values and expressions for the mean powers. The expression for the maximum mean power is given for the considering system.

On the Direct Electromagnetic Scattering Problem by an Impenetrable Partially Coated Obstacle Embedded in a Chiral Environment

pp. 285-306 | DOI: 10.5890/JVTSD.2023.09.004

K. H. Leem, G. Pelekanos, V. Sevroglou

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Abstract

In this paper the direct scattering problem by an impenetrable obstacle embedded in a given homogeneous background chiral medium is studied. Incident electromagnetic waves are propagated in a homogeneous chiral environment. We assume that the chirality measures of the background and exterior medium are both distinct positive constants. Our scatterer has a smooth boundary that is divided into two open disjoint parts for which an impedance boundary condition on the one part of the boundary, and a perfectly conducting boundary condition on the other part, are satisfied. Uniqueness results for the above scattering problem, using the Bohren decomposition into Beltrami fields, are established. Consequently, we introduce a \emph{chiral Calderon} operator, for which its basic properties are proved, and its connection with the existence of our problems solution is presented. The well-posedness of our problem is completed by proving the continuous dependence of the solution on the boundary data. Finally, some discussion and conclusions are given.

Wear Estimation of High Speed Train from Motion Measurements

pp. 307-326 | DOI: 10.5890/JVTSD.2023.09.005

Anni Zhao, Jian-Qiao Sun

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Abstract

Active controls have been used to enhance the stability of high speed trains against hunting instability. The control system uses motion measurements of the train for decision making. These measurements can also be used to estimate wear of the wheel due to dynamic interactions with the rail. In this paper, we present an approach that makes use of the well-known extended state estimator to estimate interaction forces between the wheel and rail from motion measurements. Archard's wear model is adopted to compute the damage of the wheel. To take advantages of motion measurements further, we treat Archard's wear model as a surrogate to generate a large set of wear data from simulated motions. This is valuable because it is expensive and time consuming to collect real data of wheel wear. We develop a neural networks model to directly link train motions with the wheel wear. With the neural networks model, we can then predict the wheel wear from motion measurements of high speed train in service. It is expected that the neural networks wear model can help engineers to develop more effective maintenance schedule.

Dynamics and Bifurcations in a Quadratic Nonlinear System with Univariate Product Vector Fields

pp. 327-397 | DOI: 10.5890/JVTSD.2023.09.006

Albert C. J. Luo

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Abstract

In this paper, nonlinear dynamics of dynamical systems possessing bivariate quadratic vector fields is presented. The bivariate quadratic vector field is a product of two different-variable univariate functions in two directions. The dynamical systems with two crossing-variable product bivariate vector fields are presented, and the corresponding global dynamics of such dynamical systems is presented. The hyperbolic and hyperbolic-secant flows with directrix flows are discussed. From the infinite-equilibriums, the inflection sink (or source) bifurcation is presented for the switching of hyperbolic flow and saddles with hyperbolic-secant flow and sink (or source). Parabola-saddle bifurcations are for the switching of saddle and hyperbolic-secant flow with center and hyperbolic flow, which is called the saddle-center switching bifurcation. Inflection diagonal-saddle bifurcations are presented for the switching of the network of saddle and sink (or saddle and source) with hyperbolic and hyperbolic-secant flows.

JVTSD Volume 7, Issue 4

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Predator-Prey Model with Intraguild Predation in an Uncertain Environment

pp. 399-417 | DOI: 10.5890/JVTSD.2023.12.001

Prabir Panja, Sailen Gayen, Dipak Kumar Jana

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Abstract

In this paper, a prey, intermediate predator and top predator interaction model has been developed. Here all parameters of the model have been considered as triangular fuzzy number. Positivity and boundedness of solutions of the proposed model have been investigated. Possible equilibrium points of the model are determined and also local stability of the model around these equilibrium points have been studied. Global stability of the model around the interior equilibrium point is also studied. Conditions for the existence of Hopf bifurcation have been investigated with respect to $\alpha$ (degree of uncertainty). It is found that the uncertain values of the parameters have a great influence in the solution of the proposed model. From the analysis of the model, it is observed that intra-species competition rate of prey as well as intermediate predator can be stabilized the system. It is also observed that the harvesting rate of intermediate predator has the ability to stabilize the system. Some complex behaviour of the system have been seen due to the increase of death rate of top predator species. Finally some numerical simulation results have been presented to verify the analytical findings.

Analysis of an Undamped Mass-Spring System with Generalized Piecewise Constant Argument

pp. 419-429 | DOI: 10.5890/JVTSD.2023.12.002

Marat Akhmet, Duygu Arugaslan ¸Cincin, Zekeriya Ozkan

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Abstract

In this study, we consider an undamped mass-spring system that experiences piecewise constant forces and analyze the solutions of this system. We investigate the solutions of undamped mass-spring system by using the method of steps. In addition to investigating the solutions, stability and convergency analyses are performed for the solutions of nonhomogeneous undamped mass-spring system. The results are stated in terms of the parameters of the systems. Simulations are given to illustrate and support the findings for different values of the parameters.

Design and Implementation of the Digital Twin Software Platform for Complex Rotor System

pp. 431-445 | DOI: 10.5890/JVTSD.2023.12.003

Ze-wen Cui, Zhong Luo, Lei Li, Kai Sun, Dong-ze Wu

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Abstract

Aiming at the problems that the complex rotor system is difficult to carry out and monitor due to variable load and bad working conditions, the design method of software platform based on digital twin technology is studied, and the architecture and main function realization of digital twin software platform are explored from six aspects: physical layer, virtual layer, data layer, functional layer, client layer and connection layer. A method to establish the digital twin model of rotor system integrating geometric model and mechanism model is proposed. The digital twin model of the existing rotor test-bed is constructed. Based on the digital twin software platform of the rotor test-bed, the rationality of the design and implementation method is verified by comparison with the experiment.

Mathematical Modeling and System Identification of a Piezo-actuated, Cantilever Beam with Interferometric Measurement

pp. 447-461 | DOI: 10.5890/JVTSD.2023.12.004

Jordan Kochavi, Siyuan Xing

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Abstract

Laser interferometers are often adopted in high-precision motion control systems but seldom used for experimental vibration analysis. This is partly because their installation and mounting are invasive to dynamical systems as opposed to non-contact position sensors such as vibrometers. However, as the industry moves towards light manufacturing structures out of economical and environmental considerations, metrology systems that already utilize laser interferometry, such as profilometry in semiconductor manufacturing, may benefit from interferometer measurement for vibration analysis. This study investigates the use of laser interferometry for vibration analysis and system identification through a piezoelectrically actuated cantilever beam mounted with a retroreflector. The dynamics of the beam, which include the piezoelectric actuator and optical measurement components are modeled through the Euler-Bernoulli beam theory. This leads to a continuous system, which is then transformed into a discrete system represented in a state-space form, through the method of separation of variables. The frequency response at the retroreflector location is obtained through the Laplace transformation of the state-space form. A recursive adaptive filter following the ARMAX structure is formulated to identify the transfer function of the discrete system from its random noise excitation. The transfer function and its frequency response is analytically predicted, then compared to the simulation and experimental results from the adaptive filter. The high-precision measurement of interferometers is well-suited for applications of signal processing such as system identification.

Effect of Flow Disruptors on the Performances of a Cantilever Piezoelectric Energy Harvester

pp. 463-470 | DOI: 10.5890/JVTSD.2023.12.005

Edoardo Rubino, Jordan Meciej

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Abstract

This study aims to determine the effect of a flow disruptor on the performances of a cantilever piezoelectric energy harvester invested by an airflow. The purpose of the flow disruptor is to increase the turbulence intensity of the incoming flow and therefore the momentum transferred to the piezoelectric beam. The height of the flow disruptor and the distance between the flow disruptor and the energy harvester were investigated to determine the optimal configuration. Results indicate that for an energy harvester with a frontal area of $\mathrm{\sim}$18 cm${}^{2}$ (7 cm by 2.54 cm), the flow disruptor should have a height of 4 cm and should be placed 13 cm away from the harvester. Also, a shift in the frequency of vibration occurs when the flow disruptor is placed in front of the harvester.

Comprehensive Modal Analysis for In-Plane Free Vibrations of High-Speed Annular Disks

pp. 471-507 | DOI: 10.5890/JVTSD.2023.12.006

Ehsan Sarfaraz, Hamid R. Hamidzadeh

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Abstract

In view of the vast potential applications of flexible thin rotating disks, the knowledge of their vibration characteristics has been considered by many investigators. Rotating disks are the main components in various machinery applications, such as space structures, flywheels, torsional disk dampers, grinding wheels, turbine rotors, circular saw blades, computer storage devices and brake systems. Dynamic response and stability of rotating disk depend on its rotational speed. The knowledge of the in-plane vibration of rotating disks is also essential for the design of spinning disks. In most cases, to rotating a disk at a certain speed, a knowledge of modal vibrations and critical speeds of the disks are essential. An analytical solution is investigated to determine in-plane modal vibration characteristics of high speed rotating annular disks. A systematic approach based on the established governing equation for the linear in-plane free vibrations of disks is developed, and the displacements and stresses compatibilities are considered. The disk material is elastic homogeneous, thin, and isotropic and is rotating at constant angular speed. The developed analytical solution is obtained by implementing the two-dimensional plane stress theory. In this research, several possible boundary conditions for the annular disks are investigated, and natural frequencies and mode shapes of rotating disks are computed. The mode shape functions for displacements and stresses in the radial and circumferential directions are determined. In addition, variations of nondimensional modal frequencies versus a wide range of dimensionless rotational speeds for several radius ratios are presented.

JVTSD Volume 8, Issue 1

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Investigation of Dynamic Load Characteristics for Rolling Bearing

pp. 1-13 | DOI: 10.5890/JVTSD.2024.03.001

Si-Jia Zheng, Zhong Luo, Yao-Jia Yang, Di Xu, Xiao-Lu Yan

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Abstract

For cylindrical roller bearing, a dynamic model considering the degree of freedom of the rollers is established to analyze the influence of the external load and clearance on dynamic characteristics of rolling bearing. Firstly, the load distribution curve is compared with Hou’s test data to verify the validity of the bearing dynamic model. Then, load distribution curves and the fixed point load sequences are calculated under different clearances. And the angular position equations of bearing components at the moment of the load mutation occurs at the fixed points on inner and outer raceways are established for analyzing the law of the load sequence variation. Finally, the load sequences of the danger points of inner raceway and outer raceway are calculated under the coupling effect of radial load and unbalanced load. The results show that the load sequence varies periodically and the period is determined by the angular position deviation of the fixed point when the first and the last contact occurs during the point rotates in one turn. Without considering the unbalanced load, the load distribution curve can completely envelop the contact load sequence at the fixed point of the inner ring raceway, and with the increase of the clearance, the span of the envelope peak of the load sequence decreases and the height increases.

Large Eddy Simulation of Gas Flow Fluctuation in Tee Junction Pipes

pp. 15-31 | DOI: 10.5890/JVTSD.2024.03.002

Tao Di, Xu Sun, Shun Zhou, Jun Xiao, Dongying Wang, Yue Shu, Lingren Yu, Jiaxing Sun, Yuxuan Wu, Zifeng Yu, Hong Zhang

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Abstract

Gas transmission pipeline vibration is mostly caused by gas flow fluctuation, and the disturbance of the gas flow through the tee junction pipes is one of the reasons for the large gas flow fluctuation. Large Eddy simulation (LES) method is applied to gas flow fluctuation in tee junction pipes in this paper. Firstly, the models of numerical simulation and the geometric parameters are displayed, in addition to the governing equations of compressible flow in LES. Subsequently, accuracy and applicability of LES method for compressible internal flow problem are validated and the optimal subgrid-scale (SGS) model, DSM SGS model, was selected by comparing the reference values with the values calculated of each of the SGS models. Finally, to reveal how the gas flow fluctuation in tee junction pipe (or with a blind end) vary with the influencing factors, LES method and DSM SGS model are applied to simulate the flow of compressible fluid (methane) in the tee junction pipes. The influencing factors are flow velocity and branch internal diameter, and in the case of tee junction pipes with a blind end, branch length is also taken into account.

Towards Finding the Conformal Invariance of the Multi-point Vorticity Statistics in 2d Turbulence

pp. 33-45 | DOI: 10.5890/JVTSD.2024.03.003

Vladimir N. Grebenev, Alexandre N. Grishkov

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Abstract

The conformal invariance of certain statistics in the inviscid twodimensional turbulence is derived. For this we investigate the transport equation for the two-point probability density functions of vorticity from the infinite Lundgren-Monin-Novikov hierarchy and give the conditions under which the probability measure is conformally invariant. This is an extension of our previous analyses of the onepoint statistics, which also paves the way for further generalisation to arbitrary n-point statistics.

Energy Harvesting of a Unimorph-Piezoelectric Portal Frame Using Component Mode Synthesis

pp. 47-66 | DOI: 10.5890/JVTSD.2024.03.004

Nyesunthi Apiwattanalunggarn

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Abstract

This paper describes a methodology for modeling a unimorphpiezoelectric portal frame based on electromechanical energy formulation of the Euler-Bernoulli beam with axial deformations, the fixedinterface component mode synthesis by Craig and Bampton, and the Rayleigh-Ritz method. An assembled model obtained from this approach is the reduced-order model in terms of generalized modal coordinates without dealing with finite-element model during modeling formulation. The operating frequency of the portal-frame energy harvester can be reduced significantly from a cantilevered-piezoelectric energy harvester. The total-voltage output of the portal frame is the sum of voltage outputs from each substructure due to in-phase voltage outputs of each substructure. The presented approach can be used systematically to study an internal resonance of the portal frame when both piezoelectric-material nonlinearity and geometric nonlinearity are included.

Wear Detection Method of Electric Power Field Safety Appliances based on Deep Learning

pp. 67-76 | DOI: 10.5890/JVTSD.2024.03.005

Zhu Shi, Hao Wu, Zhong-yang Jin, Hong Song

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Abstract

Aiming at the problem of low detection accuracy of small and medium targets and occluded targets in power field, a new wear detection method improved SBC YOLOv5 is proposed. This method is based on expansion convolution, and uses multi-scale pooling operation and MHSA self attention module to improve the spatial pyramid pooling layer, so that it can obtain more abundant receptive fields. Secondly, it uses feature bridging operation and CARAFE operator to improve the Neck network, so as to improve the network’s ability to extract and compensate semantic features. Finally, it uses CIoU to opti- mize the network’s loss function and improve the regression ability of the model. The experimental results show that the wear detec- tion method SBC established in this paper The average accuracy mAP(Mean Average Precision) of YOLOv5 is 82.3%, the recall rate is 81.5%, and the detection speed FPS is 44. Compared with original YOLOv5, YOLOv4, and Faster RCNN, the mAP values of YOLOv5 are increased by 1.5%, 10.27%, and 25.21%, respectively. It can effec- tively improve the detection accuracy of small targets and occluded targets, and meet the real-time and accuracy requirements of wear detection at power operation sites.

Dynamics and Bifurcations in a Quadratic Nonlinear System with Univariate Product Vector Fields, Part II

pp. 77-154 | DOI: 10.5890/JVTSD.2024.03.006

Albert C. J. Luo

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Abstract

In this paper, nonlinear dynamics of the product-quadratic systems with self-quadratic and crossing-quadratic vector fields is presented, which is the study continuation of product-quadratic systems with two product-quadratic vector fields. With a self-quadratic field, the stability and bifurcations of product quadratic systems are dis- cussed. The saddle-sink bifurcation for saddle and sink is discussed, and the saddle-source bifurcation for saddle and source is presented. The saddle-saddle bifurcations of the first kind are presented. The appearing bifurcation conditions for sink-source and saddle-saddle are discussed. The inflection sink (or source) bifurcations are pre- sented for the switching bifurcations for hyperbolic flow and saddles with hyperbolic-secant flow and sink (or source). With a crossing- quadratic vector field, the dynamics and bifurcations for such a quadratic system are discussed. The saddle-center appearing bifur- cations are presented through the parabola-saddle bifurcations. The center-center bifurcation and the saddle-saddle bifurcation of the sec- ond kind are discussed through the hyperbolic sink-source and circu- lar sink-source bifurcations. The up-parabola-saddle bifurcations are for the switching of the center and hyperbolic flow with saddle and hyperbolic-secant flows. The down-parabola-saddle bifurcations are for the switching of the center and hyperbolic-secant flow with saddle and hyperbolic flows. The parabola-saddle on the infinite-equilibrium is called the switching bifurcations of saddle and center.

JVTSD Volume 8, Issue 2

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The Building Blocks of the Spiral Arms in Galaxies

pp. 155-171 | DOI: 10.5890/JVTSD.2024.06.001

Mirella Harsoula, Athanasios C. Tzemos

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This is a review paper on the main theories of orbital mechanism that support the spiral arms in the case of grand design galaxies as well as in the case of barred spiral galaxies. While, in the first case stable periodic orbits form families of precessing ellipses that produce spiral density waves similar to those observed in real grand design galaxies, in the second case the spiral structure is supported by sticky chaotic orbits along unstable asymptotic manifolds. This mechanism is valid in the case of one pattern speed as well as of two different pattern speeds, for the bar and the spiral structure. Finally, in the case where the bar rotates much faster than the spiral arms, perturbed precessing ellipses can support spiral density waves.

Statistics of Topological Defects in Finite One-Dimensional Structures based on the Kibble Zurek Mechanism

pp. 173-181 | DOI: 10.5890/JVTSD.2024.06.002

Vasileios Vachtsevanos, Hariton M. Polatoglou

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Abstract

The appearance of topological defects in the solid state is well observed and studied with the Kibble Zurek mechanism. However, the size of the systems and the eect that size has on the defect density is not yet properly studied and understood, as it is a problem of mathematical complexity. In this work, a number of simulations will be performed in order to see how the system's size aects the statistics of defects for dierent cooling rates. We have found that strange behaviors arise for specic sizes and cooling rates, which might hint at the existence of a correlation between the size and the defects. We also simulated the system for a variety of random ight sizes, in order to more accurately nd the divergent behaviour and under which conditions it appears.

Vehicle and Pedestrian Detection Based on Improved YOLOv5s

pp. 183-194 | DOI: 10.5890/JVTSD.2024.06.003

Shun-Yong Zhou, Hao Zhu, Xue Liu, Ya-Lan Zeng, Si-Cheng Li, Yang-Ming Luo

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An updated YOLOv5s algorithm for vehicle and pedestrian identification is proposed to address the variety of vehicle and pedestrian targets in road traffic under complex environments. First, the network’s nonlinear capability is improved with the addition of the GELU activation function; Second, the hybrid pyramid pooling structure (HSPPF) is utilized in the backbone network to lessen the loss of feature layer information; Finally, transfer learning and the EIoU loss function are incorporated to enhance the model’s accuracy and speed of convergence. The experimental findings demonstrate that the enhanced algorithm can reliably identify targets such as vehicles and pedestrians. Its mAP value is 94.0%, 1.8% faster than before the enhancement, and its detection speed is 80.6 FPS. It is more suited for complex real-world traffic circumstances and has higher detection accuracy and speed when compared to other algorithms.

Analysis of the Dynamical Behavior of a Modified Cubic-Map with a Discrete Memristor

pp. 195-205 | DOI: 10.5890/JVTSD.2024.06.004

Laskaridis Lazaros, Christos Volos, Ioannis Stouboulos

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Abstract

In this work, a memristor-based modified Cubic mapping model is presented by coupling a discrete memristance function with a modified Cubic map. This model is based on the memristor, which was discovered by Chua in 1971, as the fourth fundamental electrical component in addition to resistance, capacitance, and inductance. To investigate system’s dynamical behavior a set of nonlinear tools has been used, such as bifurcation and maximal Lyapunov exponent diagrams as well as phase portraits. Interesting phenomena related to nonlinear theory have been observed such as, hyperchaotic behavior, regular (periodic and quasiperiodic) and chaotic orbits, as well as route to chaos through the mechanism of period doubling and crisis phenomena.

LMI-based State Feedback Control of the Underactuated InertiaWheel Inverted Pendulum to the Unstable Upright Position

pp. 207-234 | DOI: 10.5890/JVTSD.2024.06.005

Hassene Gritli, Sahar Jenhani

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Abstract

One of the frequent tasks in the robotic research field is to control the position of the robot and then change its current position to the intended state. This study focuses on the position feedback control through a state-feedback control law of an underactuated Lagrangian-type robotic system, called the inertia wheel inverted pendulum (IWIP), to its unstable upright state. Furthermore, using a rescaled dynamic model that describes the difference between the nonlinear dynamics and its approximate linear model, and based on the S-procedure, the Young inequality and the Schur complement lemma, we develop conditions on the feedback gain for the stabilization using two different methodologies. These designed methodologies are realized based on the Linear Matrix Inequality (LMI) techniques. We show that an initially obtained bilinear matrix inequality is converted into an LMI via some mathematical tools. Moreover, we introduce some further LMIs in order to minimize the feedback gain’s size. Finally, we show some numerical results to illustrate the effectiveness of the proposed state-feedback control law for stabilizing the underactuated IWIP.

An Energy Based Description of Complex Brain Network Dynamics

pp. 235-248 | DOI: 10.5890/JVTSD.2024.06.006

Chun-Lin Yang, Nandan Shettigar, C. Steve Suh

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Abstract

Biophysiological measurements are inadequate in making explicit the various properties of the brain at the network level for the reasons that these properties are complex functions of the electrochemical gradient and the cumulative area of triggered ion channels. Neuron dynam- ics, synaptic dynamics, and neural electrophysiological coupling have been considered in [1]. This study continues the work presented in [1] and considers biophysiological (local) and brain network (global) dynamics. The general framework for dynamic complex networks [2] is followed to describe brain network dynamics in this study. At the local level, individual neuron dynamics is defined using energy by considering each neuron as a type of biological battery. The poten- tial energy is the charge of ions a neuron holds which is the mem- brane potential. The kinetic energy is the change of ion charge in time introduced by the ion flux across the membrane that induces the change of membrane potential. Degree-of-couplings, DOC k and DOC J, are indicators of the coupling strength of connected neurons. Since the energies of individual neurons in the network are normally distributed, brain network dynamics can be described by information entropy as a function of the probability of the individual neuron en- ergies at the global level. Information entropy is also used to measure the degree of synchronization of the firing of action potential.

Distributed Position and Velocity Delay Effects in a Van der Pol System with Time-periodic Feedback

pp. 249-272 | DOI: 10.5890/JVTSD.2024.06.007

Ryan Roopnarain, S. Roy Choudhury

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Abstract

The effects of a distributed delay on a parametrically forced Van der Pol limit cycle oscillator are considered. Delays modeling time lags due to a variety of factors in self-excited systems, have been considered earlier in the context of modification and control of limit cycle and quasiperiodic responses. Those studies are extended here to include the effects of periodically amplitude modulated distributed delays in both the position and velocity. A normal form or ‘slow flow’ is employed to search for various bifurcations and transitions between regimes of different dynamics, including amplitude death and quasiperiodicity. The existence of quasiperiodic solutions then motivates the derivation of a second slow flow. A detailed comparison of the results and predictions from the second slow flow to numerical solutions is made. The second slow flow is also employed to approx- imate the amplitudes of the quasiperiodic solutions, yielding close agreement with the numerical results on the original system. Finally, the effect of varying the delay parameter is briefly considered, and the results and conclusions are summarized.

JVTSD Volume 8, Issue 3

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Dual Authentication on a Secure Communication Channel to Image Transmission

pp. 273-284 | DOI: 10.5890/JVTSD.2024.09.001

Lucas G. Nardo, Erivelton Nepomuceno, Janier Arias-Garcia, Thomas M. Chen, Denis N. Butusov

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Abstract

Chaotic systems have been widely adopted for image encryption as means of securely transmitting confidential information. However, literature suggests that some encryption algorithms and transmission channels may be vulnerable, which raises concerns about the efficacy of using chaotic systems for image encryption. To address these concerns, this paper proposes an approach based on dual authentication to enhance information security and mitigate image attacks. The proposed method involves encrypting the image using a secure cipher and mixing the resulting encrypted image with a chaotic signal generated by two synchronized R¨ossler systems before transmitting it over a channel. The original image can be recovered by reversing the encryption and transmission process. The method was successfully tested using the Mean Structural Similarity Index (MSSIM), and a second security layer showed an increase in entropy, which is a strong indicator of good random properties. The proposed scheme has been proven to be secure in encrypting and transmitting benchmark images.

Nonlinear Dispersion Dynamics of Optical Solitons of Zoomeron Equation with New $\varphi ^{6}$-Model Expansion Approach

pp. 285-307 | DOI: 10.5890/JVTSD.2024.09.002

Muhammad Abubakar Isah, Asif Yokus

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Abstract

One of the equations describing incognito evolution, the nonlinear Zoomeron equation, is studied in this work. In a variety of physical circumstances, including laser physics, fluid dynamics and nonlinear optics, solitons with particular properties arise and the Zoomeron equation is a single example of one such situation. The method of $\varphi^6$-model expansion allows for the explicit retrieval of a wide range of solution types, including kink-type solitons, these solitons are also called topological solitons in the context of water waves, their velocities do not depend on the wave amplitude, others are bright, singular, periodic and combined singular soliton solutions. The outcomes of this research may improve the Zoomeron equation's nonlinear dynamical features. The method proposes a practical and effective approach for solving a large class of nonlinear partial differential equations. The nonlinear dispersion behavior is analyzed for different values of the magnitude, which physically represents the wave velocity, from the parameters of the generated traveling wave solutions. Interesting graphs are employed to explain and highlight the dynamical aspects of the results, and all of the obtained results are put into the Zoomeron equation to show the accuracy of the results

Chaos in Optimal Communications: Theory and Experimental Demonstration

pp. 309-316 | DOI: 10.5890/JVTSD.2024.09.003

Jonathan N. Blakely, Marko S. Milosavljevic, Ned J. Corron, Seth D. Cohen, Casey Fendley

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Abstract

The properties of nonlinear dynamics and chaos are shown to be fundamental to optimal communication signals subject to two practical and realistic design requirements: (i) operation in a noisy environment and (ii) simple hardware implementation. The first requirement implies the receiver should include a matched filter, i.e. a filter that maximizes the signal-to-noise ratio when receiving the corresponding matched waveform. The second requirement can be met by employing a simple infinite-impulse-response (IIR) filter as the matched filter. Here we examine the waveforms matched to stable IIR filters characterized by all-pole transfer functions. This class of filters contains many of the most popular and widely used filter families, including Butterworth, Chebyshev (type I), and Bessel. We find that these waveforms are chaotic in the sense that they are deterministic and characterized by a positive Lyapunov exponent. Interestingly, a return map using samples from any such waveform takes the form of a shift map. We derive this map theoretically and present an experimental reconstruction of it using an actual electronic filter and its matched waveform. A practical consequence of chaos in these waveforms is the potential for simple and efficient signal generation using chaotic oscillators.

Attractivity of Time-periodic Solutions of Ginzburg-Landau Equations of Superconductivity and Numerical Simulations

pp. 317-328 | DOI: 10.5890/JVTSD.2024.09.004

Mei-Qin Zhan, Kening Wang

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Abstract

It is well-known that the Ginzburg-Landau equations admit at least three time-periodic solutions. One of them describes the non-super- conductive (or normal) state and the other one describes the super- conductivity state. In this paper, we investigate the uniform bound- edness and attractivity of these time-periodic solutions. Moreover, numerical approximations to time-periodic solutions are also pre- sented.

Resource Allocation Strategy for Power Safety Tools with Fuzzy Systems and Edge Computing

pp. 329-340 | DOI: 10.5890/JVTSD.2024.09.005

Bin Liu, Zhongqiang Luo, Xiang Dai, Hongbo Chen

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Abstract

As a solution to solve data congestion and improve the quality of service, edge computing emphasizes that the data of local data sources should be processed according to their locations. In order to solve the problem that the efficiency of traditional power safety management tools is low in the management cycle process that affects business delivery, this paper proposes a resource offloading algorithm with multiaccess edge computing (MEC) server as the core and cloud collaborative work. Firstly, the application of MEC in the scenario of new infrastructure power safety tools is studied.Then, a three-layer edge computing architecture of terminal, edge and cloud is constructed with resource scheduling, and the attributes of incoming tasks, network transmission and computing resource performance in this scenario are dynamically considered. Finally, the fuzzy logic coordinator is used to determine which services are cached at the edge and which tasks are executed in the cloud. The simulation experiment results show that the superiority of the proposed resource offloading algorithm in the service performance of power safety tools is verified from multiple performance indexes such as service time, task failure rate, and resource utilization rate.

A Novel Chaotic System with Hyperbolic Tangent Terms and Its Application to Random Bit Generator and Image Encryption

pp. 341-353 | DOI: 10.5890/JVTSD.2024.09.006

Savvas Kosmidis, Christos Volos, Lazaros Moysis, Efthymia Meletlidou

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Abstract

In this work the study and use of a continuous chaotic dynamical system with no equilibria is presented. In more details the proposed 3-D system has two hyperbolic tangent terms and it has both self excited and hidden attractors. The behavior of the system is studied numerically through phase portraits, bifurcation diagrams and Lyapunov exponents. Also, the design of a random bit generator, based on the chaotic system, is presented. The randomness of the generated bitstream is tested through NIST 800-22. Finally, the random bit generator is used in an image encryption application. The encryption scheme is resistant to various attacks, as it is thoroughly shown.

Analysis and Control of the Chaotic Behavior of the Compass-Type Bipedal Walker: Comparison between two Controllers

pp. 355-377 | DOI: 10.5890/JVTSD.2024.09.007

Essia Added, Hassene Gritli, Safya Belghith

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Abstract

The goal of this work is to control the chaotic behavior of the passive dynamic gait of the bipedal compass walker. An impulsive hybrid nonlinear system models the dynamic gait of the compass walker. This impulsive hybrid nature is regarded as being exceedingly complex since it has the potential to produce undesirable phenomena like chaos and bifurcations. We rst demonstrate that the passive dynamic gait exhibits multiple period-doubling bifurcations that result in chaos, while altering the slope angle of the walking surface and the length of the lower leg segment. After that, in order to control chaos and achieve a one-periodic walking behavior, two controllers (a PD plus gravity compensation and an improved PD plus gravity compensation) are employed and a comparison between them is achieved. Finally, we present some simulation results demonstrating the eectiveness of the two suggested control strategies in stabilizing the chaotic passive gait of the compass-like bipedal walker.

JVTSD Volume 8, Issue 4

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Numerical Optimization of Continuous--Time Neural Network Equations: --A New Application of Hopf Bifurcation Analysis

pp. 379-390 | DOI: 10.5890/JVTSD.2024.12.001

Cheng Luo, Guo-Cheng Wu, Hu-Shuang Hou

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Abstract

Many neural networks can be modeled by differential equations. They hold rich dynamics and numerical methods are generally used for numerical simulations. It becomes challenging to determine an appropriate time step--size for long time numerical simulations. This paper suggests a new application of Hopf bifurcation analysis for numerical optimization. First, a discrete--time neural network is obtained by Euler scheme. Then the time step--size is set as a bifurcation parameter and the frequency domain analysis approach is used to determine the critical value. Periodic solutions are obtained by the harmonic balance method. The direction of Hopf bifurcation and sufficient stability conditions are given. Finally, it can be concluded that the method is efficient to find the critical time step--size such that a continuous--time system can be approximated stably.

Three Level Image Encryption Using a Modulo-based Chaotic Map

pp. 391-403 | DOI: 10.5890/JVTSD.2024.12.002

Nikolaos Charalampidis, Christos Volos, Lazaros Moysis, Ioannis Antoniades, Ioannis Stouboulos

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Abstract

This paper investigates the issue of chaos-based image encryption. Based on the $z$-shaped fuzzy number, the exponential function, and the modulo operator, a 1-D chaotic map is constructed and studied. This map contains areas with constant chaotic behavior and high Lyapunov exponent values. A statistically secure pseudorandom bit generator is designed based on the new map, and it is used in the encryption process. A three level color image encryption technique is introduced that is based on a shuffling process to the rows and columns of an image, followed by a modulation process in each pixel, and finally by an XOR operation. The resulting ciphertext image is then shown to be resistant to a variety of attacks, including histogram, correlation, and entropy analysis, NPCR and UACI measures, cropping and tampering attacks, and transmission noise. This is demonstrated by applying the encryption to a set of images.

The Effect of Intra- and Inter-Ring Couplings in Leaky Integrate-and-Fire Multiplex Networks

pp. 409-416 | DOI: 10.5890/JVTSD.2024.12.003

K. Anesiadis, J. Hizanidis

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Abstract

We study the dynamics of identical Leaky Integrate-and-Fire (LIF) neurons on a multiplex composed of two ring networks with symmetric nonlocal coupling within each ring and one-to-one connections between rings. We investigate the impact of different intra-ring coupling strengths in the two rings for attractive and repulsive inter-ring coupling and show that they can lead to subthreshold oscillations. The corresponding parameter spaces where this phenomenon occurs are determined numerically. Moreover, we show that depending on whether the couplings between the two rings are attractive or repulsive, the interaction produces qualitatively different behavior in the synchronization patterns and the mean frequency profiles.

Experimental Evaluation of the Isolation Effectiveness of Elastic Rail Shock Isolators (ERSI) for Protecting Weapons from Severe Underwater Shock

pp. 417-427 | DOI: 10.5890/JVTSD.2024.12.004

Dattatraya R Hipparkar, Sunil Chandel

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Abstract

Shock isolation is a critical issue from the point of view of the problem of weapons stored inside submerged platforms from severe underwater shocks. The shock loads may result from the underwater explosion of a nuclear warhead, mines, and bomb nearby submerged platform. These underwater explosions would generate shock loads up to several hundred g's and must protect weapons from severe damage to keep them operational under such circumstances. The most efficient method for reducing shock levels transferred to weapons is shock isolation, which has received little attention from many researchers. Therefore, an Elastic rail shock isolator (ERSI) design was implemented to isolate underwater weapons stored inside submerged platforms to certain acceptable limits. In this study, the prototypes of ERSI were manufactured, and tests were carried out to investigate the isolation effectiveness under laboratory test conditions. The experimental setups were designed, and tests were performed on the universal shock test machine (USTM) equipped with instrumentation to measure the parameters during shock motion, i.e., acceleration and relative displacement of mass. On USTM, a shock input of 170g for 3 ms was characterized, and prototypes were subjected to shock tests to evaluate the performance of ERSI. Finally, the data collected during the shock test was analyzed and compared with analytical results to conclude on isolation performance of ERSI. Thus, the weapon protection was qualified for increasing combat reliability and endurance under attack.

Research on Automatic Detection of Epilepsy based on Sliding Time Windows

pp. 429-447 | DOI: 10.5890/JVTSD.2024.12.005

Zhiyi Jing, Ying Wu, Yeyin Xu

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Abstract

Epilepsy is a highly prevalent neurological disorder worldwide, and the automatic detection of epileptic activity in clinical practice is a significant focus of researchers. In this study, we construct a high-performance model for normal and epileptic electroencephalogram signals using a convolutional neural network architecture called Shallow ConvNet based on the CHB-MIT dataset. The model achieves a maximum classification accuracy of 98\%. We also investigate the effects of different data slice and sample sizes on the model performance. Results show that larger data slice sizes can improve accuracy and generalization ability to a certain extent, while increasing the sample size of the training set only improves accuracy but not generalization ability. The best overall performance is achieved by the classifier trained with a slice size of 5 seconds and a training set sample size of 500. These findings provide theoretical guidance for the clinical application of automatic epilepsy detection.

Modified Gradient Descent Approach Involving Caputo Fractional Derivative with Metaheuristic Optimizer

pp. 443-453 | DOI: 10.5890/JVTSD.2024.12.006

Rinki Sharma, Priyanka Harjule

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Abstract

In this paper, a modified Gradient Descent algorithm is investigated, which involves Caputo fractional derivative and a metaheuristic optimizer. Mathematical formulation for convergence analysis of the proposed algorithm is done in this study. Further, this article aims to enhance the initialization for better performance of existing fractional Gradient Descent algorithm. In this study the significance of using fractional derivative in Gradient Descent is also examined. Caputo fractional derivative is preferred due to its memory and non-locality properties. Metaheuristic algorithms are efficient in providing approximate results in fewer iterations. The fractional Gradient Descent algorithm with metaheuristic initialization is given for faster convergence. Further, the fractional Gradient Descent algorithm with a firefly optimizer is applied on the quadratic loss function. Results shows that this hybridization of the firefly optimizer and fractional order Gradient Descent converges in fewer iterations as compared to the existing algorithms.

Wind Velocity Induced Stable and Unstable Periodic Oscillations in a Harmonically Excited Aeroelastic Energy Harvester

pp. 455-470 | DOI: 10.5890/JVTSD.2024.12.007

Bo Yu

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Abstract

This study explores the periodic oscillations occurring in a piezoelectric energy harvester exposed to a blend of fluid and harmonic force, with a specific focus on the system’s responses to varying wind velocity. A coupled single degree of freedom model for the electromechanical system is presented. For the external forces, both periodic excitation and aerodynamic galloping are considered. The nonlinear differential equations are discretized, and the expressions of periodic responses are derived through the implicit mapping method. The periodic responses are calculated using the Newton-Raphson method. By assessing the eigenvalues of the resultant matrix derived from the mapping structures, the stabilities and bifurcations of these periodic responses are determined. Furthermore, the study investigates how the displacement and voltage nodes of the energy harvester respond to variations in free stream velocity and excitation amplitude. Maximum eigenvalue magnitudes are also presented for stability assessment. Additionally, utilizing the periodic nodes of displacement and voltage, the harmonic amplitudes are calculated using Fast Fourier Transform, illustrating their variation with changes in free stream velocity. Finally, the study compares implicit maps and numerical simulations for both stable and unstable responses.

JVTSD Volume 9, Issue 1

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CombOpNet: a Neural-Network Accelerator for SINDy Open Access

pp. 1-20 | DOI: 10.5890/JVTSD.2025.03.001

Siyuan Xing, Qingyu Han, Efstathios G. Charalampidis

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Abstract

In the present work, we develop and assess a compact neural-network architecture called hereafter the Combinatorial Operation Neural Network (CombOpNet) which is designed to mitigate the curse of dimensionality of Sparse Identification of Nonlinear Dynamics (SINDy). Within CombOpNet, nonlinear terms in dynamical equations are represented by a chain of multiplication of univariate functions. These functions correspond to neurons of a multi-layer neural network which allows the construction of nonlinear terms in dynamical equations by employing forward propagation. This way, the CombOpNet can form and perform summations of all possible combinations of univariate functions now using far fewer weights, which themselves can reconstruct the elements in the coefficient matrix of SINDy. If $n$ and $p$ denote the number of dimensions and order of nonlinearity, respectively, the present method reduces the number of SINDy coefficients from $n\binom{n+p}{n}$ to $\mathcal{O}(n^3p)$. This reduction facilitates the scalability of SINDy, making SINDy applicable to multidimensional systems such as power grids and climate models. We discuss the implementation of CombOpNet in Tensorflow, and demonstrate its applicability to several complex nonlinear dynamical systems with an eye towards solving high-dimensional problems.

Multi-Scale Modeling of Proteins and Cells: A Protocol for Modeling of Complex Systems

pp. 21-46 | DOI: 10.5890/JVTSD.2025.03.002

Sheldon (Xiaodong) Wang

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Abstract

One of the major challenges in today's science and engineering fields is how to handle complex systems. Reductionist principles have helped scientists and engineers to develop uncanny an understanding of the universe ranging from mechanical to electro-magnetic properties and phenomena. Ever since that famous quote from Albert Einstein, ``God does not play dice," people often wonder what happened to obvious uncertainties in life and in nature. What would have happened if the Asteroid missed the Yucatan Peninsula in Mexico and the Earth 65 million years ago? The research in chaotic nonlinear systems seems to point us in a direction that even the deterministic nonlinear system can produce unpredictable results. Is it possible that when a large number of factors or entities interact nonlinearly with each other, they eventually yield a completely different system which is quantifiable with an entirely different set of phenomenological rules? Of course, the intermediate stage is characterized by a so-called positive Lyapunov exponent, fractals, and bifurcations. It is not difficult to imagine that a large or infinitely large positive Lyapunov exponent tends to produce a stochastic or random system. Overall, the accurate description of physical, chemical, and biological phenomena over a wide range of spatial and temporal scales is extremely difficult if not feasible. Nevertheless, although the intricate nature of turbulence poses seemingly insurmountable challenges to scientists and engineers with its spatial and temporal chaotic behaviors, many useful strategies have been discovered and implemented in various engineering applications. In the same spirit, in this study, various hierarchical modeling techniques have been explored in multi-scale and multi-physics modeling of proteins and cells. In addition, singular value decomposition, the key concept of importance to many reduced order modeling strategies, is reiterated with respect to four fundamental subspaces, namely, left null space, column space, null space, and row space for a rectangular matrix representative of any linear space tangent to a curved space or differentiable manifold. Using the singular value decomposition, it is possible to identify the hidden spatial and temporal correlations and patterns between variables and material properties. Hopefully, a computational protocol with phenomenological rules derived from experimental and computational approaches can be established for the modeling of complex systems.

Grey-Box Modeling Method for Single Degree of Freedom Nonlinear Vibration Isolation System

pp. 47-61 | DOI: 10.5890/JVTSD.2025.03.003

Zhi-Ao Wang, Zhong Luo, Yun-Peng Zhu, Guang-Ze Zhou, Bing Yu

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Abstract

The present study aims to investigate a new modeling method of single degree of freedom nonlinear vibration isolation system. Grey-box theory is used to model the system. Grey-box model is a combination of white-box model and black-box model. The white-box model is a simple component of vibration isolation system expressed by the differential models. In contrast to the white-box model, the black-box model is a NARX (Nonlinear AutoregRessive with eXogenous input) model, which is used to represent the complex structural components in the vibration isolation system that cannot be built with differential model. Based on the interface analysis, the grey-box model of vibration isolation system is obtained by integrating the white box model and the black box model. Compared with traditional physical modeling and finite element simulation, the method proposed in this paper is more rapid and cost saving. In addition, the grey-box modeling method can also be applied to the design of vibration isolators. Finally, a single degree of freedom nonlinear vibration isolation system is taken as an example to verify the correctness of the proposed method. The results of the study indicate that the proposed method is effective.

Results on ψ-Hilfer Implicit Fractional Boundary Value Problem with Impulses

pp. 63-75 | DOI: 10.5890/JVTSD.2025.03.004

M. Latha Maheswari, K. S. Keerthana Shri

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Abstract

The $\psi$-Hilfer implicit fractional boundary value problem with impulses is investigated in this paper. The qualitative analysis is carried out by means of Krasnosel'skii's fixed point theorem and the Banach contraction principle. An example is provided to help interpret our results, which are also analysed graphically.

Numerical Simulation and Regression Trends in Magnetohydrodynamic Nanofluid Flow Past a Stretching Sheet

pp. 77-88 | DOI: 10.5890/JVTSD.2025.03.005

P. Priyadharshini, M. Vanitha Archana

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Abstract

Recent progress in industries have led to nanofluids with superior thermal attributes to clear fluids. These improvements act as motivation for the present work, which emphasizes the heat and mass transfer properties of magnetohydrodynamic incompressible nanofluid flow towards a stretching sheet with the addition of thermal radiation. The mathematical model is framed in the knowledge of fundamental conversation laws and followed by transmuted into a dimensionless form employing similarity variables. The set of these converted equations are numerically treated through Wolfram language. An influence of germane parameters on boundary layer are scrutinized and graphically visualized to deliver the applicability of the present model. Furthermore, the machine learning technique for predicting the physical nature of flow is innovated as a novelty. In place of the classical simulation method, this work uncover the new technique to anticipate the physical quantities more accurately. The findings demonstrate that the thermal profile is an escalating term of the nonlinear radiation parameter. The outcomes are authenticated by comparing the current exploration with some earlier studies in certain instances and the reliability is highlighted with a aid of table format. The multiple linear regression accurately predicted the measurement of engineering concerns with the minimal error $10^{-3}$. The present optimization technique delivers a robust and intellectual perspective on industrial processes, such as solar technologies, polymer extrusion, metal processing, rubber sheet production, etc.

Hermitian Symmetry of a Dynamic Structure with Odd Elasticity

pp. 89-95 | DOI: 10.5890/JVTSD.2025.03.006

Z.C. Feng

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Abstract

We present the wing flutter model as a dynamic structure with odd elasticity. The wing flutter model is an elastically supported airfoil in the flow. The lift force contributes to the non-Hermitian stiffness to the existing elastic support. The stability analysis of the flutter model demonstrates the onset of oscillations due to the odd elasticity. Surprisingly, we found linear coordinate transformations such that the equations of motion in the new coordinates are Hermitian: with symmetric mass matrix and symmetric stiffness matrix.

Different Types of Maps Route to Chaos in Bi-infinite Symbol Space with Strong Chaotic Features

pp. 97-104 | DOI: 10.5890/JVTSD.2025.03.007

Hena Rani Biswas, Ruma Rani, Sakibul Islam, Umme Habiba Khatun

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Abstract

The main purpose of this study is to introduce a generalization of the shift two-sided map, that is, the generalized two-sided shift map. In this paper, we discuss periodic points that are dense in $\Sigma_{m}$ regarding the generalized shift map $\sigma_{n}$: ${\Sigma}_{m}\to{\Sigma}_{m}$. We consider a particular property of the dynamical system namely, the topologically transitivity. Here, we prove that the generalized shift map is topologically mixing and hence is topologically transitive on ${\Sigma}_{m}$. Few strong chaotic properties of the generalized shift map have been discussed. We know that the two-sided shift maps are automorphisms and the one-sided shift maps are endomorphisms. These maps can be conjugate or semi-conjugate to some automorphisms or endomorphisms which admit appropriate Markov partitions. We also discuss other maps such as $\alpha $-map and $\beta $-map are chaotic in bi-infinite symbol space.