On the study of vibration of a supported railway rail using the semi-analytical finite element method
An improved rail vibration model based on the semi-analytical finite element (SAFE) method has been developed, which allows multiple layers of support and the accurate shape of the rail cross-section to be considered in the modeling. Rail supports are treated as a continuous layer of equivalent springs connected to the rail foot. Three different assumed support conditions corresponding to no support; rail pads; and rail pads, sleepers and ballast have been modeled. By determining the track parameters from a field test, this model is demonstrated to be able to determine the dispersion relations and the forced responses of both free and variously supported rails. Further, the effect of rail damping including frequency-dependent viscous damping and frequency-independent structural damping on rail vibration responses is investigated. The effect of the adopted discretization strategy on the calculation is also studied. Model results are compared with predictions from the Timoshenko beam-based rail models with the same support conditions. The results show that track support dynamic stiffness can be incorporated into the developed SAFE rail model which can then be used to represent the real track situation at a site; the rail support can significantly affect rail dispersion and frequency responses below 1. kHz; the Timoshenko beam-based rail models provide an inadequate prediction of rail vibration response, particularly in the lateral direction, if response at specific frequencies is required; the rail damping has limited impact on rail vibration responses; and the number of elements has insignificant effect on the calculated rail responses and wave dispersion relations, especially away from the excitation point.