The time domain moving Green function of a railway track and its application to wheel-rail interactions

When dealing with wheel-rail interactions for a high-speed train using the time domain Green function of a railway track, it would be more reasonable to use the moving Green function associated with a reference frame moving with the train, since observed from this frame wheel/rail forces are stationary. In this paper, the time domain moving Green function of a railway track as an infinitely long periodic structure is defined, derived, discussed and applied. The moving Green function is defined as the Fourier transform, from the load frequency domain to the time domain, of the response of the rail due to a moving harmonic load. The response of the rail due to a moving harmonic load is calculated using the Fourier transform-based method. A relationship is established between the moving Green function and the conventional impulse response function of the track. Properties of the moving Green function are then explored which can largely simplify the calculation of the Green function. And finally, the moving Green function is applied to deal with interactions between wheels and a track with or without rail dampers, allowing non-linearity in wheel-rail contact and demonstrating the effect of the rail dampers.