TITLE: Padé-Type Approach to Nonlinear Random Vibration Analysis

AUTHOR: Roy-R-Valéry. Spanos-P-D.

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

SOURCE: Engineering Probabilistic Mechanics, 6, pp. 119-128, 1991.

ABSTRACT: 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 simulation data.