STABILIZED SOLUTION OF STRUCTURAL DYNAMICS IN WAVELET SPACES

A stabilized wavelet-based scheme is used to simulate vibration of structures. The method is a kind of projection scheme, where operators are projected to wavelet space. Derivatives with respect to time are directly projected to wavelet space; then the whole solution is captured in thewavelet space. Consequently the solution in time is attained by an inverse transform. Using a fewer number of initial sampling points in the simulation lead to a larger time steps in modeling. This feature will increase the speed of computation. In fact operators in the wavelet space aresparse and narrow banded. This means a cost effective computation, which is desirable in simulation, especially in the multi-degrees of freedom systems (a kind of semi modal analysis). Finally effectiveness and accuracy of the proposed method are demonstrated by some examples, including single degree of freedom systems.

Keywords:

Adaptive Wavelet , SDOF and MDOF Dynamical systems , Numerical Solution