Analyzing Nonstationary Random Response of a SDOF System under the Evolutionary Random Excitation by Wavelet Transform

For evolutionary random excitations, a general method of analyzing nonstationary random responses of systems was presented in this paper. Firstly, for the evolutionary random excitation model, the evolutionary power spectrum density function （EPSD） of a random excitation was given by wavelet transform. Based on the EPSD, the nonstationary responses of a SDOF system subjected to evolutionary random excitations were studied. The application and validity of presented method were illustrated by numerical examples. In numerical examples, the recently developed stochastic models for El Centro （1934） and Mexico City （1985） earthquakes which preserve the nonstationary evolutions of amplitude and frequency content of ground accelerations were used as excitations. The nonstationary random mean-square responses of a SDOF system under these two excitations were evaluated and compared with simulated results.