Extreme Response of the Linear Oscillator with Modulated Random Excitation

Abstract

Corotis and Marshall (1977) have studied the extreme response of a single degree of freedom linear oscillator to Gaussian white noise modulated by a deterministic function in the form of a sum of exponential terms. This form of excitation provides a broad range of descriptive capabilities for different physical situations — in particular for earthquake excitation. In this paper the question of uniqueness of definition of the envelope of such a process is raised, following Hasofer (1979) and a solution presented. It is then argued that the use of stationary formulae for estimating the uperossing rate of such a response at high levels might seriously underestimate the actual rate. Exact formulae are then presented for the uperossing rate of the response and its envelope. It is shown that Vanmarcke’s (1975) concept of “qualified uperossings” can be extended to the case under consideration, resulting in a considerable improvement in the estimation of the reliability function of the response. Finally numerical results are presented to illustrate the main conclusions.