Integration Algorithm for Covariance Nonstationary Dynamic Analysis of SDOF Systems Using Equivalent Stochastic Linearization

Random vibration theory is the natural way to deal with some dynamic actions whose nature is deeply random, such as wind, earthquakes or sea waves. Moreover only in a few cases exact solutions are available, so that approximate solutions are usually adopted: Stochastic equivalent linearization is one of the widely used. Its application needs specific numerical techniques, whose complexity is greater in nonstationary cases than in stationary ones and that are usually approached in time domain instead of frequency domain. In this paper, an iterative integration algorithm is proposed in order to solve this problem for single-degree-of-freedom (SDOF) oscillators, using the evolutive Lyapunov equation for nonlinear mechanical linearized system by stochastic linearization technique. It updates linearized system matrix coefficients step by step, by an iterative procedure based on a predictor–corrector technique. The proposed algorithm is described and applied to an hysteretic Bouc–Wen SDOF system excited by a modulated filtered white noise nonstationary process. The accuracy and computational cost are analyzed showing the efficiency of the proposed integrating procedure.