Stochastic response analysis of nonlinear systems under Gaussian inputs

Abstract

In this paper the extension of Itô's rule for the case of vector real valued functions of the response of nonlinear systems excited by zero-mean Gaussian white noise processes is presented. A suitable particularization of the vector function, in order to obtain the statistical moments of every order to the response, is treated, obtaining the differential equations of the response moments in an elegant and compact form. Polynomial expansion and closure schemes are framed in the context outlined here in order to obtain an effective procedure from a computational point of view. An application to a trigonometric nonlinear system, solved in the literature by the stochastic averaging method, is treated here by the moment equation approach using the polynomial expansion of the nonlinear terms in order to evidence the validity of this approach.