Improved stochastic linearization method using mixed distributions

Abstract

A new procedure for the random vibration analysis of hysteretic structures using stochastic equivalent linearization is reported. Its aim is to improve the prediction of the response obtained by conventional Gaussian linearization technique. To this purpose, mixed discrete-continuous Gaussian distributions are used taking into account the bounded nature of the non-linear restoring force. The simple but important property of the mixed distribution is its linearity, which allows the use of the previous results obtained by the Gaussian hypothesis, avoiding the need of employing non-Gaussian continuous distributions or other time-consuming techniques such as local Monte Carlo simulations. Closed-form expressions of the new linearization coefficients for the Bouc-Wen-Baber model are then provided. The relative weights of the discrete and Gaussian distributions are calculated in dependence of the degree of non-linearity in each time step. The comparison of the results with previously published ones obtained by simulation shows a good agreement, providing a substantial improvement of the method with respect to the conventional Gaussian technique with the same calculation effort.