Keywords: travelling load, wave propagation, track-train interaction.

This paper regards some new, and from the engineering point of view most important, phenomena which should be of interest to experts in high-speed railways. The dynamic interaction of high-speed rail vehicles with the track is very complex. Some effects are still not well understood even by specialists in this field. A wide palette of models is required to cover all aspects of the topic. So, for the study of certain phenomena, it is appropriate to substitute the contact forces exacted by a wheel, which in reality are spread over a region of contact, by a Dirac force applied in the point of contact. Even a description based on two Heaviside functions, e.g. in the case of track-train interaction, can give important insight, because for such model assumptions analytical solutions are available. A crucial point in the analysis is the proper application of the Sommerfeld conditions, both in the case of long, theoretically infinite, tracks and of a finite but closed wheel-tyre. Frequently the contact load is described by a harmonic Dirac force moving at constant speed. Then, in the speed-frequency plane, several regions of qualitatively different behaviour exist. The boundaries between those regions consist of critical resonance curves, which are dependent on the track, rail or wheel-rim modelling. They differ, even in their number, for Bernoulli-Euler, Rayleigh or Timoshenko beam equations. Important experimental observations on real vehicle-track systems can be explained using these theoretical foundations. For comparison some numerical investigations are carried out.

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