A simplified weak simulation method for the probabilistic response analysis of nonlinear random vibration problems

Abstract

Numerical simulation methods are among the most used techniques to evaluate the stochastic response of engineering systems subjected to random excitations. In many practical situations the system should be integrated over long time intervals and a large number of sample trajectories need to be generated to assess the quantities of interest. In this circumstance conventional methods usually show exploding behavior or their implementation is computationally very demanding. In this paper we propose a new numerical simulation method for the probabilistic response analysis of nonlinear random vibration problems. We devise a simplified weak method having the simplicity of basically needing only three-point distributed random variable per time step for its implementation. Also, we prove that it reproduces the same statistical properties that characterize the exact solution to the linearized equation corresponding to the underlying system. This makes the method an efficient tool for stable long term simulations. Numerical experiments are carry out to illustrate the practical performance of the method.