Nonlinear Response of Structures Subjected to Stochastic Excitations via Probability Density Evolution Method

Abstract

Stochastic response analysis plays an increasingly important role in assessing the performance and reliability of engineering structures subjected to disastrous dynamic loads such as earthquakes and strong winds. In the past decade, a family of probability density evolution method (PDEM) has been developed where a completely decoupled generalized density evolution equation (GDEE) is proposed. The dimension of GDEE could be arbitrary and in most cases a reduced one-dimensional equation is adequate. This provides an efficient solution for stochastic response of complex engineering structures. In the present paper, PDEM is incorporated with the efficient representation of stochastic processes to implement stochastic dynamic response analysis of multi-degree-of-freedom (MDOF) systems subjected to stochastic excitations. Stochastic dynamic responses of linear and nonlinear base-excited systems are investigated by PDEM, the pseudo-excitation method and the Monte Carlo simulations. The Sobol' sequence is employed to generate representative white noise process, and a high-performance stochastic harmonic function representation with fewer random variables is employed to generate representative time histories of a stochastic process with specified power spectral density model. The involved seismic excitations are modeled by banded white noise, Kanai-Tajimi filtered stationary process, Clough-Penzien filtered stationary process and Clough-Penzien filtered process with non-stationary modulation, respectively. Numerical results reveal that PDEM is feasible for stochastic response analysis of MDOF nonlinear systems subjected to stochastic excitations with fair accuracy and efficiency.