Probability density evolution method for dynamic response analysis of stochastic structures

Probability density evolution method for dynamic response analysis of stochastic structures is presented. Based on the finite element method, the state equations of structural response containing random parameters are deduced. The probability density evolution equation (PDEE) of the stochastic structural response is then established by introducing the augmented state vector. Combing the precise integral method and the Lax-Wendroff difference pattern lead to a numerical solution method for the PDEE. A case study is carried out on the response of an 8-storey stochastic structure and the results are compared with those obtained by Monte Carlo method. The research shows that the probability density curves of the stochastic structural response have typical characteristics of evolution, and they are far from normal distribution. At some time instants, they even have double peaks.