Some Observations on the Random Response of Linear and Nonlinear Dynamical Systems.

摘要

This report examines two problems which are commonly encountered in the study of the response of randomly excited discrete dynamical systems. First,an extension of the method of equivalent linearization is used to obtain an approximate solution for the nonstationary response of a nonlinear system subjected to deterministically modulated stationary Gaussian random excitation. The accuracy of the approximate technique is investigated by means of Monte Carlo simulation. Secondly,an approximate method is developed for treating the first passage problem for the stationary response of a lightly damped linear oscillator excited by white noise. This method is extended to the nonstationary problem as well,and the accuracy of the approximate approach is examined. The analytical techniques developed are used to generate an earthquake-like random process which corresponds to a prescribed response spectrum.