Stochastic response of hysteretic systems

Abstract

This paper deals with approximate stochastic response of hyseretic structures under white noise excitation, based on Itǒ stochastic differential equations. Instead of the original system an equivalent nonlinear system is considered, in which the drift vector is given by a series expansion of the order n ⩾ 1 in terms of the state variables. n = 1 represents the well-known case of equivalent linearization. Components in the drift vector representing the nonanalytical constitutive equations are replaced by a cubic polynomial expansion. The hierarchy of statistical moment equations is closed by a cumulant neglect closure scheme. The method has been applied to a bilinear single degree-of-freedom system subjected to white noise excitation, for which an equivalent system with a cubic series expansion to the constitutive equation is considered. The results obtained are compared with those of numerical simulation and alternative methods, and they provide substantial improvements compared to equivalent linearization.