ABSTRACT
This paper presents an efficient calculation method for prediction of the steady-state response of a three-dimensional model of a railway track to a uniformly moving axle load of a train. The track model includes rails, pads, sleepers and a layered ground. Due to the sleepers, the model is periodically inhomogeneous along the track. The method is based on the so-called periodicity condition, which requires any two points of a rail, which are separated by the sleeper distance, vibrate with a well-defined phase lag that depends on the sleeper distance, load velocity and load frequency. Employing the periodicity condition, a closed-form expression is derived for a dynamic stiffness of the ground under a sleeper. This dynamic stiffness relates the forces induced by all sleepers on the ground to the displacement of one sleeper. It is the same for all sleepers. To demonstrate the calculation method, a short analysis is carried out of the dynamic stiffness and the displacements of the rails for a sub-critical velocity of the load.
