Nonlinear vibration analysis of structure based on wavelet perturbation method

This wavelet theory is a powerful tool for dealing with nonlinearity. To start with basic principles of the nonlinear vibration equation, this paper proposed a nonlinear restoring force model in accordance with existing model characteristic, we derived wavelet perturbation solution of nonlinear vibration equation based on wavelet transform and perturbation methods. Finally, signal-degree-of-system under earthquake as an example for the nonlinear seismic response was analyzed. The results show that the method is feasible, zero order displacement response is the largest, the first order perturbation displacement response and the second order perturbation displacement response were relatively small.