An Itô-based general approximation method for random vibration of hysteretic systems, part I: Gaussian analysis

Abstract

The cumulant-neglect closure scheme independently developed by Ibrahim and Lin is extended for determining the stationary and non-stationary response of non-linear systems with hysteric restoring force characteristics. The method is applied to the analysis of a hysteresis and model with strength and/or stiffness degradation capabilities. This model has been studied in the past by Baber and Wen for the analysis of hysterically degrading systems using equivalent linearization. The same model has also been used for stochastic seismic performance evaluation of reinforced concrete buildings. Response statistics obtained for the model by using this closure scheme are compared with results of equivalent linearization via Monte Carlo simulation. The study performed, for a wide range of degradation parameters and input power spectral density levels, shows that the Gaussian responses obtained by this approach are identical with the linearized results. This general approximation technique, however, can provide information on higher order statistics for hysteretic systems. These non-Gaussian statistics have not been made available so far by the existing approximation techniques. In this paper the Gaussian statistics are presented.