TITLE: Stochastic averaging of oscillators excited by colored Gaussian processes.

AUTHOR: Roy-R-Valery.

INSTITUTION: Univ of Delaware, Newark, DE, USA.

SOURCE: International Journal of Non-Linear Mechanics v 29 n 4 Jul 1994. p 463-475.

PUBLICATION: JA (Journal Article).

ABSTRACT: The method of stochastic averaging has been developed and applied in the past mainly based on Stratonovich-Khasminskii theorem. We examine in this paper the application of this method in the case of arbitrary colored Gaussian excitations, which can be considered as the output of multidimensional linear filters to white Gaussian noise. The method used is based on a perturbation theoretic approach of the Fokker-Planck-Kolmogorov equation, which governs the response probability density function. First, for oscillators with linear elastic forces and non-parametric excitation, it is shown that, to leading order of perturbation, the results obtained match those derived by application of Stratonovich-Khasminskii theorem in the case of broad-band excitation. Then, more general results are derived for nearly Hamiltonian systems perturbed by parametric excitations of uncorrelated colored noises. It is shown that the state probability density function is governed by a reduced equation in the `slow' Hamiltonian variable only, which depends on a number of parameters characterizing the colored noise excitations. Several examples are given for illustration. As a preliminary to these theoretical developments, the problem of determining the eigenfunctions and eigenvalues of the Fokker-Planck operator is addressed for a general class of linear multidimensional systems. (Author abstract) 19 Refs.