Keywords: train-track-bridge system, numerical simulation, dynamics of railway bridges, finite element modelling, dynamic interaction.

This paper describes the formulation, application and validation of a numerical model used by authors to simulate the dynamic interaction between a train, rail track and bridge. The model was developed to investigate the influence of dynamic effects on the vertical displacements of the Boyne Viaduct, Drogheda, Ireland. Separate models were formulated for bridge, rail track and rolling stock. The spatial lattice structure of the Boyne Viaduct was modelled as an assemblage of three-dimensional beam finite elements. The finite difference method was applied to model the rail track because of its ease of implementation. The planar rolling stock model consists of lumped masses, springs and dampers and is capable of simulating vertical motions of trains traversing bridges.

Contact between wheels and rails was modelled using the Hertzian springs. These springs allow the forces transmitted from the rolling stock to the track to be calculated as a function of time and rail penetration. The connections between track and bridge models are represented by spring elements with stiffness equivalent to sleepers stiffness.

The direct time stepping Runge-Kutta method was applied to numerical integration of the system's equations of motion. The method was chosen because of its good accuracy and because it allows the vibrations of particular bridge member to be found.

The numerical model was tested on the Boyne Viaduct. The testing involved calculation of vertical displacements, velocities and accelerations of the bridge nodes. In order to validate the model developed by the authors similar model of the test case was generated using the commercial FEM package ANSYS. Inherent ANSYS contact elements were used to represent wheel-rail contact phenomenon. The full transient dynamic analysis was carried out to establish structure response to a moving train model.

Results from both packages were compared and discussed, in particular the discrepancies between these results were considered. Selected results from authors' numerical model were presented.

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