Efficient Nonstationary Stochastic Response Analysis for Linear and Nonlinear Structures by FFT

Abstract

Based on the fast Fourier transform (FFT), an efficient and accurate algorithm was developed for improving the computational efficiency of structural responses under nonstationary stochastic excitations. In this method, the FFT technique was first adopted to accelerate the evaluation of time integration terms involving significant computational effort in the nonstationary stochastic response analysis of linear structures. Then, the proper orthogonal decomposition was used to assist the application of FFT for the generally modulated excitation by separating the frequency item of nonuniform modulation functions from the time integration terms. Further, the proposed method was extended to the nonstationary stochastic response analysis of nonlinear structures based on the equivalent statistical linearization method. Finally, numerical examples with respect to linear structures, Duffing systems, and hysteretic systems illustrated that the proposed method performs well.