Stochastic linearization technique : A new interpretation and a selective review

Abstract

Several developments in stochastic linearization are summarized in this review paper, along with the new, statistical orthogonality-based derivation of the method. A nonlinear oscillator subjected to colored noise is examined, the case of nonlinear damping is discussed, and the true stochastic linearization technique is described. The results of the latter match the exact mean square responses of a nonlinear structure. A combination of stochastic linearization with the Monte Carlo method is outlined. In addition, the accuracy of an energy linearization technique versus the newly interpreted classical scheme is examined for a Duffing oscillator subjected to white or colored noise excitations. The results obtained by the two schemes are compared in terms of percentage-wise error relative to the exact solution or relative to numerical results obtained through Monte Carlo simulation. These applications confirm the superiority of the energy linearization technique over the force linearization technique in several examples considered. In certain circumstances, however, namely for some nonlinear softening oscillators, newly interpreted conventional linearization may yield more accurate results. The method of weighing functions improves the accuracy of both methods.