Dynamic Analysis of Nonlinear Multi-degree-of-Freedom System Subjected to Combined Gaussian and Poisson White Noises

Abstract

AbstractEngineering structures are usually subjected to random excitation, which may cause nonlinear dynamic behavior. The random excitation can be modeled as Gaussian or non-Gaussian white noise stochastic process. Thus, it is of important significance to efficiently obtain the structural stochastic responses under various kinds of random excitations, including the simultaneous action of Gaussian and Poisson white noises. In this paper, a novel direct probability integral method (DPIM) is developed to address the stochastic dynamic analysis of nonlinear multi-degree-of-freedom (MDOF) systems subjected to combined Gaussian and Poisson white noises. Firstly, the probability density integral equation (PDIE) of stochastic dynamic MDOF system is derived accounting for the principle of probability conservation. The compound Poisson process is simulated by using the stochastic harmonic function method, and the techniques of probability space partition and smoothing Dirac function in DPIM are proposed to solve the PDIE effectively. Comparing with Monte Carlo simulation and path integral solutions, the probability density function results of stochastic responses of nonlinear MDOF systems under combined Gaussian and Poisson white noises indicate the high efficiency and accuracy of the proposed DPIM.KeywordsNonlinear multiple-degrees-of-freedom systemCombined Gaussian and Poisson white noisesProbability density integral equationDirect probability integral method