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.