The Analysis Of Dynamic Response Of The Viaduct System Based On Wavelet-Galerkin Method

Recently, people have began to give more and more concern to the influence of vibration induced by traffic load to around environment because of the development of track traffic and the increasing train speed in China. Therefore, in order to evaluate the environmental vibration along railway lines, it has very important practical value to analyze and calculate the dynamic response of viaduct and track system under moving load. In the dynamic system of viaduct and track, it is convenient to consider six sub-systems: the vehicle, the wheel-rail contact and the representation of excitation, the rail, the fastening system, the sleeper, the sleeper support (including ballast and substrate, or pier of viaduct). For the diversity of viaduct and track system, the interaction of every component and the material non-linear, there are no perfect methods of analysis and evaluation until now.Many problems in science can be eventually presented in the form of partial differential equations(PDEs). Although the methods used to analyze and calculate the PDEs have particular advantages, they also have some shortcomings that need to be improved. More and more experts give much concern to the dynamic response of viaduct and track system calculated by wavelet analysis because of the complexity of viaduct and track system and the limitation of traditional analysis. Usually applying wavelet to the PDEs, there are many problems as follows: (l)choose a suitable wavelet basis according to the problems that need to be dealt with; (2)design or modify a good algorithm in order to make use of the characters of the vavelet corresponding to the problems.In this paper, based on the research of wavelet transform and wavelet theory, the main research of this paper can be summarized as follows:1. Based on the theory of wavelet analysis and the finite two-scale relationequation, the scaling function and wavelet function with compact supports can be derived; and an orthonormal basis of Vj can be formed by multi-resolution analysis;2. Wavelet-Galerkin method needs calculating connection coefficients in the process of computing the PDEs, and these connection coefficients are the integral of wavelets multiplied by their derivatives. By use of the finite two-scale relation equation, the values of connection coefficients at arbitrary points on a bounded interval can be determined.3. Any span of viaduct can be considered as a simply supported beam; and the rail can be thought of as an infinite Winkler elastic foundation beam. First, the model equation is built up and the calculative function can be approximated by a finite series of shape function and coefficient function; then by use of Wavelet-Galerkin method, the numerical calculation of model equation and the dynamic response of viaduct and track system can be derived.4. There are some relative results by comparing wavelet analysis with traditional analysis; and all of these are useful to analyze and calculate the dynamic response of viaduct and track system.