First passage problem of the beam under a random stream of moving forces

Abstract The problem of first crossing of the dynamic response of a beam to the passage of a train of concentrated forces with random amplitudes is considered. Force arrivals at the beam are assumed to constitute a Poisson process of events. Thus, the excitation process idealizes vehicular traffic loads on the bridge. It is assumed that the parameters of the beam can be random. In order to obtain a crossing rate n + for the given threshold, the solution for the joint characteristic function and the joint probability density function of response (deflection and speed of the deflection) of the beam are determined. As an example, the response of a beam to stationary stream of forces is determined for some practical situations and discussed. The solutions and results presented can be used in estimations of the reliability of bridge structures.