Computational method for the dynamics of railway tracks on a non-uniform viscoelastic foundation

The foundation of a railway track may be non-uniform due to a number of reasons and this area is currently the subject of significant research. In this article, a new method has been developed for computing the responses of railway tracks based on a non-uniform foundation subjected to moving forces. This method is a coupling of an analytical model for the rail together with the sleepers and a finite element method for the foundation. In steady-state, it is supposed that the responses are unchanged when the moving forces come and go away from a larger interval of the railway track which contains a non-uniform zone. The dynamical stiffness matrix (DSM) of the foundation is computed by the finite element method and it is transformed to meet the steady state boundary condition. On the other hand, the rail together with the sleepers and rail pads are modelled by a periodically supported beam subjected to moving forces. This analytical model leads to a relation between the reactions forces and the displacements of the sleepers. This relation describes also the degrees of freedom (DOFs) of the nodes of the foundation at the contact surfaces with the sleepers. Then, a transformation technique has been developed in order to substitute the analytical relation into the DSM. Finally, the responses have been computed by using the transformed DSM. This method is a coupling of the analytical and numerical methods. Therefore, it has reduced all DOFs of the track components (sleepers, rail, and rail pads) which gives a significant advantage in computational time.