Formulation of Equations of Motion for a Simply Supported Bridge under a Moving Railway Freight Vehicle

Based on energy approach, the equations of motion in matrix form for the railway freight vehicle-bridge interaction system are derived, in which the dynamic contact forces between vehicle and bridge are considered as internal forces. The freight vehicle is modelled as a multi-rigid-body system, which comprises one car body, two bogie frames and four wheelsets. The bogie frame is linked with the car body through spring-dashpot suspension systems, and the bogie frame is rigidly linked with wheelsets. The bridge deck, together with railway track resting on bridge, is modelled as a simply supported Bernoulli-Euler beam and its deflection is described by superimposing modes. The direct time integration method is applied to obtain the dynamic response of the vehicle-bridge interaction system at each time step. A computer program has been developed for analyzing this system. The correctness of the proposed procedure is confirmed by one numerical example. The effect of different beam mode numbers and various surface irregularities of beam on the dynamic responses of the vehicle-bridge interaction system are investigated.

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