Non-Gaussian Linearization Method for Stochastic Parametrically and Externally Excited Nonlinear Systems

A new practical non-Gaussian linearization method is developed for the problem of the dynamic response of a stable nonlinear system under both stochastic parametric and external excitations. The non-Gaussian linearization system is derived through a non-Gaussian density that is constructed as the weighted sum of undetermined Gaussian densities. The undetermined Gaussian parameters are then derived through solving a set of nonlinear algebraic moment relations. The method is illustrated by a Duffing-type stochastic system with/without parametric noise excited term. The accuracy in predicting the stationary and nonstationary variances by the present approach is compared with some exact solutions and Monte Carlo simulations.