Stationary Response of a Randomly Parametric Excited Nonlinear System

Abstract

This paper presents a review of three truncation schemes for the problem of the infinite hierarchy of moment equations and an investigation of the stationary response of a nonlinear system under a broad band random parametric excitation. The validity of the truncation methods is discussed together with the conditions for preservation of moment properties. One of these schemes is employed to truncate the dynamic moment equations of a nonlinear single-degree-of-freedom system subject to a broad band random parametric excitation. The influence of inertia, stiffness, and damping nonlinearities is discussed and closed-form solutions are obtained for each case. The preservation of the response moment properties is confirmed for certain solutions while it fails for the remaining ones. The invalidity of these solutions is not necessarily attributed to the inaccuracy of the used truncation method as it may be due to the fact that the system may not be able to achieve a stationary response.