AUTHOR: Roy-R-Valéry. Spanos-P-D.
INSTITUTION: Univ of Delaware, Newark, DE, USA.
SOURCE: Engineering Probabilistic Mechanics, 6, pp. 119-128,
A new approach is proposed for the prediction of the response
statistics of nonlinear systems under additive and multiplicative
white noise excitation.
The prime concept of this approach is to use ordinary
perturbation expansion techniques, not for representing the random system
response itself, but its statistical moments.
Specifically, it is shown that the
infinite hierarchy of stationary
moments equations may be solved in a closed form by expressing each unknown
moment in the form of a perturbation expansion in powers of the parameter
quantifying the system nonlinearity.
Then, by recasting the series solutions
by means of Padé-type transformations, quite reliable
approximations are found for even strongly nonlinear systems.
The method is applied on various nonlinear systems.
The derived results are validated by comparison with pertinent Monte Carlo