Wavelet Analysis Method For Solution To Structural Dynamic Responses In Time-history Analysis

Wavelet analysis is a novel mathematical theory and method proposed in the last 20 years. It is regarded as a breakthrough of Fourier analysis because it has good time-frequency localization and flexible time-frequency windows. As a powerful tool of non-stationary signal processing, wavelet analysis also suitable to process earthquake ground motion acceleration. Applying wavelet theory to structural dynamic responses, the best suitable wavelet function needed in present paper was selected for establishing the analytic expression of earthquake ground motion acceleration from a wide variety of wavelet functions, which can bring convenience for analytic expression.This paper, a comprehensive discussion of the development status, advantages and difficulties of elasto-plastic analysis of earthquake response for RC structures is given. The application steps of general numerical integration and basic characteristics are mainly discussed, and the advantages and disadvantages and feasibility are compared. As the most widely used numerical integration method in dynamic structural history analysis, we must explore a series of problems such as convergence of the algorithm, stability, solution accuracy and overshooting of calculation result when these methods used in earthquake response equation. In addition, these methods have the algorithm damping generated from the inherent attributes of difference scheme that is difficult to control and sensitive to the Accuracy of the final solution dramatically. Moreover, the applicability of a specific integral method depends on the type and extent of nonlinear loads and characteristics of a variety of factors. The discussions show that numerical integrations have application limitations.Wavelet theory and application is an important aspect of research by using wavelet base to approach different types of functions. Comparing with the general numerical integration methods, the simulation of earthquake ground motion acceleration for solving structural dynamic responses has its own characteristics. The analytical expression of structural dynamic responses is obtained by selecting the function of second-order Cardinal B-Spline wavelet which contributes to the establishment of the accurate solution of structural dynamic responses. In this paper, a MATLAB procedure is written for the seismic response of the SDOF elastic structure. The analysis shows that the error only comes from the simulation of earthquake ground motion acceleration. Solutions to structural dynamic responses with this method effectively overcome the shortcomings of numerical integration methods. The proposed method is not only suitable for elastic analysis, but also suitable for elasto-plastic analysis.