Vol. 3, No. 4 (2014): Regular Issue

Innumerable mechanical structures including vibrating profiles, sandwich plates, platforms, thin uniperiodic shells, laminated windshells, isotropic and orthotropic platesor even multibody systems exhibit complex dynamic behavior. Analysis of the corresponding phenomena involves interesting mathematical and experimental methods that are sometimes used in parallel. Mostly, a dynamical transient response of any of the enumerated complex structures leads to the unpredictable states that need to be described and predicted. For this reason, the Special Issue extends selected papers presented during the international conference on “Dynamical Systems-Theory and Applications” hold in December 2–5, 2013 in Lódź, Poland. Main areas of modern experimental and numerical analysis taken into consideration by authors of these papers could be mentioned: bifurcations and chaos in dynamical systems, stability of dynamical systems, original numerical methods of vibration analysis, non-smooth systems, engineering systems and differential equations, control in dynamical systems, asymptotic methods in nonlinear dynamics,vibrations of lumped and continuous systems,dynamics in life sciences and bioengineering. A brief description of contents of this Special Issue follows.

The general approach to engineering of systems in oil and gas industry from the aspect of their automation and use of information technologies including design and experiment result analysis on the base of mathematical models requires involving newest technologies of artificial intelligence to obtain the most effective results. In this paper application of artificial intelligence methods such as neural networks for optimization of drilling process and automation of log curves digitization has been proposed. A hybrid neural network on the base of radial basis network learning by k-means algorithm has demonstrated the highest efficiency for solution of these problems regarding classification and pattern recognition.

he problem of stationary viscous in compressible fluid flow around the cylinder has been analyze d by means of the asymptotic methods. The fluid flow equations are considered in the variables "stream function-a vortex". Asymptotic vortex in the boundary layer near the boundary of the cylinder for average and large Reynolds numbers has been investigated. The equation of the interior boundary layer for stream function has been made by means of using the method of matched asymptotic expansions. The properties solution of the given equation are investigated by means of numerical methods under the additional condition of slipping on the boundary of the cylinder.

The experimental results for the vibrating NACA0015 profile elastically supported in a translation and rotation for a set of increasing Mach numbers of the airflow are presented. The profile was placed in the aerodynamic tunnel of the Institute of Thermomechanics ASCR. The support properties of the profile were modified by three additional masses to control the eigenfrequencies corresponding to transversal vibrations and verified by the identification of the complex eigenvalues (eigenfrequencies, damping) for zero flow velocity in laboratory. The transversal free vibrations as the time functions are graphically depicted for stable vibrations and in the cases of the starting flutter. The start of the flutter was determined from free vibrations of kinematically excited profile. The complex eigenvalues were identified as the functions of Mach number including corresponding limits of the system aeroelastic stability.

Design of multivariable control systems for complex technical plants with several interrelated channels and controlled variables is difficult problem. Usually here it is necessary to provide either independent (autonomous, unrelated) or coherent control of output variables. This design problem can be solved by using the analytical method implying exact, dynamical decomposition of the multivariable plant to the set of an independent single input–single output channels. The dynamic decomposition method is based on decomposing property of the adjunct matrix and provides realized of control action as function of output variables, reference input and measured disturbances (control on output and inputs) of the system. The efficiency of this analytical method is shown by the numerical example of control system design for the turbojet engine of the gas-pumping station with three interrelated channels.

Riser handling is a special operation performed by a dedicated, specialized lifting equipment operated from a production platform or vessel. A mathematical model of the system is developed, which allow us to simulate the loads acting on the lifting equipment as well as riser elements. The rigid finite element method (RFEM) is applied to discretize the system, consisting of long and flexible components like riser and various rope systems. Large deformations are common conditions in such systems and operations, which have to be accounted in the analysis. For the problem described in the paper, an FPSO (Floating Production, Storage and Offloading Unit) vessel consists of a dedicated riser pull-in winch. An another pipeline installation vessel (PLV) is used for the construction work related to riser handling. The load transfer between FPSO pull-in winch an PLV lifting winch is critical for the project specification and the design input. On the basis of calculated loads, the design of the riser pull-in winch can be concluded. A dedicated software developed enables for an user-friendly definition and execution of the riser handling analysis. Based on developed models and results obtained, the design conditions can be formulated. With the aid of developed mathematical model and the computer program, an example simulation of the riser installation is performed.

This paper deals with vertical mechanical oscillation of symmetric and asymmetric systems with different kinematic excitation. The solution was carried out using numerical and experimental methods. The subject of analysis were the influence of geometry, production asymmetry and unbalanced excitation on the vibration of solid bodies in the system of flexibly bonded solids taking into account the boundary conditions and the type of loading (application to the oscillation of vehicles). Numerical solutions were performed using the ADAMS program. Experiments were performed on a laboratory model. The aim was to verify the applicability and suitability of different methods and procedures for the investigation of vertical oscillation of the mechanical system of bodies.

The main focus of interest in the report is the specific irregular character of the motion in the system with an elastomeric element being a part of the frictional damper. The solution to this problem is based on the assumption that the material of the elastomeric element is non-compressible and its properties are described by Mooney-Rivlin model of the first order. Additionally, the values of the coefficients are chosen on the basis of the experiments described in references. The form of the equation of motion, which has been written by use of the non-compressiblity condition, testifies that vibrations of the system have the strong non-linear character. The numerical calculations by use of Gear's method, have given the evidence that after more than ten thousands of periods the irregular motion is present. For the case of the calculation of dissipative energy by acting dry friction between the elastomer and an aluminum element, as well as by the viscous damping, the equation of motion has been supplemented with suitable elements. It has been affirmed that the irregular motion is present only in the case of the system that exhibits the low level of damping. The detailed experiment research work on the elastomeric friction damper, in the frequency range up to 10Hz and different levels of temperature, confirms the strongly non-linear character of the motion.

In this study, the transient dynamics of a sandwich plate with post impact zone is examined. The dynamic response of the sandwich plate is simulated by using the finite element code ABAQUS. The damage mechanics approach implemented into ABAQUS via cohesive elements is applied to model the debonding propagation under impulsive loading. To demonstrate the effectiveness of the FE model developed, a foam-cored sandwich plate with an initial penny-shaped impacted region is modelled. The influence of the skin-to-core debond on the global nonlinear dynamics of the sandwich plate is studied in detail.

Thin linearly elastic Kirchhoff-Love-type circular cylindrical shells with a periodically micro - inhomogeneous structure in circumferential direction (uniperiodic shells) are investigated. At the same time, these shells have constant structure in axial direction. The aim of this contribution is to formulate some new mathematical non-asymptotic averaged models for the analysis of selected dynamic problems for the shells under consideration. These, so-called, tolerance models are derived by means of a certain extended version of the known tolerance (non-asymptotic) modelling of micro-heterogeneous media presented in [Tomczyk, B. and Woźniak, C. (2012), Tolerance models in elastodynamics of certain reinforced thin-walled structures. In: Kołakowski, Z. & Kowal-Michalska, K. (eds.), Statics, Dynamics and Stability of Structures, vol.2, Technical University of Lodz Press, Lodz, 123-153]. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, the tolerance model equations proposed here have constant coefficients depending also on a cell size. Hence, these models make it possible to investigate the effect of a length scale on the global shell dynamics. Moreover, a certain homogenized (asymptotic) model, being independent of a microstructure size, is also derived applying the extended tolerance averaging technique proposed in the above mentioned monograph.

The article deals with solution of the motion equations of plate. The rectangular plate is loaded by elastic rod which influences rectangular plate with force. The direction of the force is perpendicular to the face upper surface of the rectangular plate. The solution is derived for isotropic and orthotropic material. The solution of the motion equations has no analytical solution. The new approximation of the solution based on the transformation of integral equations to system of algebraic equations is presented.

The main object of the present study is to investigate the mechanical behavior of laminated car windshield in the case of a pedestrian head impact. Windshield Finite Element model consist one layer o f P VB and two layer s of glass. The layer of P VB was modeled in a few cases: as elastic, elasto-plastic, "low-density foam" and hyper elastic material model. The layers of glass we remodeled as "brittle cracking" material model included in Abaqus simulation environment. Both of layers was modeled as solid. Examined also two type of PVB mesh elements: " 3 D Stress " and " Cohesive ". In addition, consideration was two types of connection between glass and PVB layers: first merge and second tie connection. Analysis was performed with different types of mesh. Radial mesh proved to be better than rectangular mesh to reflect the phenomenon of cracking glass. Furthermore, the peak value of the head form linear acceleration has been tested for different thickness and material models of PVB layer.

Free vibration and flutter analyses of two types of high aspect ratio aircraft wings are presented. The wing is idealised as an assembly of bending-torsion coupled beams using the dynamic stiffness method leading to a nonlinear eigenvalue problem. This problem is solved using the Wattrick-Williams algorithm yielding natural frequencies and mode shapes. The flutter analysis is carried out using the normal mode method in conjunction with generalised coordinates and two - dimensional unsteady aero dynamic theory of Theodorsen. This is essentially a complex eigenvalue problem in terms of both air-speed and frequency. The flutter determinant is solved by an iterative procedure covering a wide range of air-speeds and frequencies. The computed natural frequencies, mode shapes, flutter speeds and flutter frequencies are compared and contrasted for the two type of aircraft wings and some conclusions are drawn.