AUTHOR: Roy-Valery-R. Spanos-P-D.
INSTITUTION: Univ of Delaware, Newark, DE, USA.
SOURCE: Journal of Applied Mechanics, Transactions ASME v 60 n 2
Jun 1993. p 358-365.
PUBLICATION: JA (Journal Article).
ABSTRACT: Spectral densities of the response of nonlinear systems to
white noise excitation are considered. By using a formal
solution of the associated Fokker-Planck-Kolmogorov
equation, response spectral densities are represented by
formal power series expansion for large frequencies. The
coefficients of the series, known as the spectral
are determined in terms of first-order response
Alternatively, a J-fraction representation of spectral
densities can be achieved by using a generalization of
Lanczos algorithm for matrix tridiagonalization, known as
the recursion method. Sequences of rational
of increasing order are obtained. They are used for
numerical calculations regarding the single-well and
double-well Duffing oscillators, and Van der Pol type
oscillators. Digital simulations demonstrate that the
proposed approach can be quite reliable over large
variations of the system parameters. Further, it is quite
versatile as it can be used for the determination of the
spectrum of the response of a broad class of randomly
excited nonlinear oscillators, with the sole prerequisite
being the availability, in exact or approximate form, of
stationary probability density of the response. (Author
abstract) 21 Refs.