Dynamic response of a beam to a train of moving forces driven by a translated Poisson process

Abstract

Dynamic response of a beam to a random train moving forces driven by a so-called translated Poisson process is considered. The commonly used model of the counting process driving the random train of loads due to highway traffic is the Poisson process. Other, more adequate models of highway traffic loads are renewal processes, for example an Erlang renewal process (Ashton, 1966). In this paper the inter-arrival times of forces (vehicles) are assumed to have a translated (shifted) negative-exponential distribution. Such a renewal counting process, called a translated Poisson process, is known to be an adequate model of highway traffic (Haight, 1963). The problem is converted into that for modal responses by normal mode technique. In time domain approach the integral expressions for a mean value and the mean square of the response involve the renewal densities (Iwankiewicz, 1995; Jabłonka and Iwankiewicz, 2021). However, since for the translated Poisson process no exact solution for the renewal density exists, this renewal density is determined approximately, using a Gaver–Stehfest method (Gaver Jr, 1966; Stehfest, 1970). The mean value and variance of the response are determined by numerical evaluation of integrals and verified against direct Monte Carlo simulations. The results are also compared with those for a train of moving forces driven by a Poisson and by an Erlang process.