Probabilistic response of an elastic perfectly plastic oscillator under Gaussian white noise

The response of an elastic perfectly plastic oscillator under zero mean Gaussian white noise excitation is studied in this paper. Considering the works of previous studies, a closed form expression of the mean maximum of the plastic drift is given assuming that the plastic process is equivalent to a Brownian motion. In order to better describe the plastic drift a probabilistic model is proposed for the yield increments which occur in clumps. To estimate the input parameters of this model, three methods, based on numerical computations of some relevant integrals, are presented. Alternatively, these parameters can be estimated, more conveniently, according to the results obtained more recently in the literature with the Slepian model approach. The results of numerical simulations show a quite satisfactory agreement with theoretical predictions.