Vibrations of the beam due to a load moving with stochastic velocity

The aim of this work is to give an approach for obtaining the probabilistic characteristics of the beam response due to a load moving with stochastic velocity. It is assumed that the load is modelled by a set of point forces of random amplitudes, the inter-arrival times are random variables that constitute the Poisson stochastic process and the forces are moving along the beam with velocities that are also stochastic. The effective solution in such a case can be obtained by applying the Ito integral and the Ito differentiation rule. In this paper, the theoretical basis for such an approach is given. Analytical expressions for calculating the probabilistic characteristics of the beam response and numerical results are shown.