Vol. 1, No. 2 (2017): Regular Issue

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.

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.

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.

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.

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.