Some observations on the random response of hysteretic systems

Abstract

In this thesis, the nature of hysteretic response behavior of structures subjected to strong seismic excitation, is examined. The earthquake ground motion is modeled as a stochastic process and the dependence of the response on system and excitation parameters, is examined. Consideration is given to the drift of structural systems and its dependence on the low frequency content of the earthquake spectrum. It is shown that commonly used stochastic excitation models, are not able to accurately represent the low frequency content of the excitation. For this reason, a stochastic model obtained by filtering a modulated white noise signal through a second order linear filter is used in this thesis. A new approach is followed in the analysis of the elasto-plastic system. The problem is formulated in terms of the drift, defined as the sum of yield increments associated with inelastic response. The solution scheme is based on the properties of discrete Markov proms models of the yield increment process, while the yield increment statistics are expressed in terms of the probability density of the velocity and elastic component of the displacent response. Using this approach, an approximate exponential and Rayleigh distribution for the yield increment and yield duration, respectively, are established. It is suggested that, for duration of stationary seismic excitation of practical significance, the drift can be considered as Brownian motion. Based on this observation, the approximate Gaussian distribution and the linearly divergent mean square value of the process, as well as an expression for the probability distribution of the peak drift response, are obtained. The validation of these properties is done by means of a Monte Carlo simulation study of the random response of an elasto-plastic system. Based on this analysis, the first order probability density and first passage probabilities for the drift are calculated from the probability density of the velocity and elastic component of the response, approximately obtained by generalized equivalent linearization. It is shown that the drift response statistics are strongly dependent on the normalized characteristic frequency and strength of the excitation, while a weaker dependence on the bandwidth of excitation is noted.