Wheel-rail Noise Generation, Part III: Rail Vibration

Train rolling noise is generated by vibrations of both the rail and the wheel. In this paper the nature of the vibration of the rail is explored theoretically, for the frequency range important for noise generation (100-5000 Hz). Initially, a finite element model of a short length of rail is studied, from which it is established that significant cross-sectional deformation can be expected above about 1500 Hz, as has also been seen in measurements. A theoretical model of an infinite rail is next presented, based on periodic structure theory. The periodic element has an arbitrary length of 10 mm. The various waves propagating in the rail are predicted, and then are combined to give the receptances of the rail. The supported rail (on ballast, sleepers and railpads) is also considered within the same basic model, by using an equivalent continuous support. The results of the model compare favourably with measurements taken from the literature.