Computational Stochastic Dynamics Based on Orthogonal Expansion of Random Excitations

Abstract

A major challenge in stochastic dynamics is to model nonlinear systems subject to general non-Gaussian excitations which are prevalent in realistic engineering problems. In this work, an n-th order convolved orthogonal expansion (COE) method is proposed. For linear vibration systems, the statistics of the output can be directly obtained as the first-order COE about the underlying Gaussian process. The COE method is next verified by its application on a weakly nonlinear oscillator. In dealing with strongly nonlinear dynamics problems, a variational method is presented by formulating a convolution-type action and using the COE representation as trial functions.