RESPONSE STATISTICS OF NONLINEAR OSCILLATORS UNDER WHITE NOISE EXCITATION

摘要

Difficulties inherent in handling nonlinear random vibration problems are well known. While some particular exact solutions are available for specific systems under white noise excitations, many practical problems have been handled by approximate approaches such as linearization and closure assumptions. Even in these approximate procedures estimation of non-Gaussian characteristics of the responses, joint density functions and the power spectral density of response functions pose difficulties. In this paper, a new method is proposed in order to evaluate the stochastic solution of linear random differential equation. The idea was to derive suitable linear differential equations for the nonlinear terms. This way the non-linear terms in the original system get replaced by linear transformations with memory. The power spectral density of response functions so obtained show non-linear features such as multiple resonant peaks. The present paper aims to carryforward the previous investigations of the authors.