Dynamic response of an infinite beam and plate to a stochastic train of moving forces

In this paper, the problem of a dynamic response of an infinite beam and a plate resting on a two-parametric foundation (“Pasternak foundation”) to the passage of a train of random forces is studied. This train of forces idealizes the flow of vehicles having random weights and travelling at the same speed. It is assumed that the occurrence process is either a Poisson process or a renewal (Erlang) process. Explicit expressions for the cumulants (semi-invariants) of the beam and plate response are provided in the case of the Poisson process and the expected value and the variance are provided in the case of the renewal process. We present two different situations and solutions: one for the arbitrary locations of the forces on the beam and another when one of the forces is located in the point in which the response of the beam has the maximum value. The first model can be used to estimate the reliability of the beam or the plate with respect to fatigue; the second model can be useful in the reliability problem of the beam or the plate with respect to the maximum response.