ABSTRACT
Several recent developments in the stochastic linearization technique are summarized in this review paper. The nonlinear oscillator subjected to colored noise is examined; the case of the nonlinear damping is discussed; the “true” stochastic linearization technique is described. The results of the latter match the exact mean square responses of the nonlinear structure. The combination of the stochastic linearization with the Monte Carlo method is outlined. In addition, the accuracy of a new linearization technique in contrast with the classical linearization scheme is examined for a Duffing oscillator subjected to white or colored noise excitations. The results obtained by the two linearization schemes are compared in terms of percentage-wise error in reference with the exact solution or numerical results obtained through Monte Carlo simulation. These applications confirm a superior performance of new linearization technique in comparison with the classical one in several examples considered. Under some circumstances, however, namely for some nonlinear softening oscillators, the conventional linearization may yield more accurate results. The method of weighing functions improves the accuracy of both the conventional and new stochastic linearization methods.
The developments described in this review mostly took place after excellent accounts on the classical version of the stochastic linearization technique, the monograph by Roberts and Spanos [49], and the review article by Socha and Soong [55], were published.
