Response of linear vibratory systems driven by renewal point processes

Abstract

Response of a linear dynamical system to a random pulse train driven by a renewal point process is considered. The response is represented as a multivariate filtered renewal process. For both ordinary and modified (delayed) renewal processes the integral equation governing the joint characteristic function of the response process is formulated. Based on this equation a recursive formula for an arbitrary joint moment of the response process is obtained. A more general model of the pulse train described by a Markov renewal (semi-Markov) process is also proposed. The set of integral equations for the characteristic function conditional on the initial state of the semi-Markov process is formulated and recursive formulae for moments are obtained. The applications of the analytical technique developed to the problem of a bridge response to highway traffic loads are presented in detail.