### Abstract:

The dynamic behaviour of a bridge, modelled as a beam, subjected to a random train of vehicles, modelled as rolling masses and then as moving SDOF oscillators, is studied. A Poisson counting process is assumed to govern the arrivals of the vehicles and the vehicles are assumed to travel at the same constant speed. The deflection function of the beam is expanded in terms of approximating functions, thus a multi-degree-of-freedom model is obtained. The interactions between the beam and vehicle model results in a coupled set of time varying ordinary differential equations of motion. The number of equations when the vehicle is modelled as a SDOF oscillators is random since another generalised coordinate must be introduced for every oscillator which passes onto the beam. This equation is only valid during the time interval that the oscillator is on the beam. The number of equations equals n+m, where n is the number of degrees of freedom for the beam and m is the random number of oscillators, which are simultaneously on the beam. A Monte Carlo simulation method is used to find the mean value and the variance of the beam deflection. A sample train of vehicles is obtained by sampling the interarrival times from the negative-exponential distribution. The equations of motion for each sample train of vehicles are solved numerically, using Matlab's ODE solvers. The computations have been performed for equal masses of the vehicles. The results obtained for a moderately short bridge and typical mean arrival rates of vehicles reveal that the transient maxima of the mean response occur within first few passage times and the response variance becomes then essentially steady. Based on the analysis of vehicle occurrence probabilities a simplified simulation technique is proposed where the train consists of first few oscillators only. The numerical results show that the proposed simplified technique allows the prediction of the maximum transient response accurately enough.