Solving method for curved track dynamic responses under a moving harmonic load

How to model a curved railway track subjected to a moving harmonic load is very important to solve its dynamic responses. Here, a periodically supported discrete curved Euler-Bernoulli beam was used to simulate dynamic responses of a curved track taken as a part of a circular structure periodically supported. The problem to solve dynamic responses of a curved track could be changed into one to be solved within one basic cell of track based on the dynamic property of periodic structures subjected to moving harmonic loads. Through introducing a curved track's vibration modes and using the modes superposition method in frequency domain, its dynamic response was expressed with a series of its bending modes displacements and torsional ones in frequency domain. The study results showed that frequency ranges for significant dynamic responses of a curved track under a moving harmonic load are near load excitation frequencies; with increase in the moving speed of load, the track's displacement responses decrease within a very narrow range near load excitation frequencies, but the track's displacement responses within most parts of the other frequency ranges obviously increase; with increase in the moving speed of load, the peaks of the track's responses change little, but time durations for significant responses become shorter; the effect of load moving speed on discrete supports' parametric excitation is significant; the vertical dynamic responses of the curved track obtained with a curved beam model agree well with those obtained with a straight beam one, so a straight beam model can be adopted to approximately study the vertical responses of the curved track; when the curved track was analyzed with a precise model, curve radius has a certain effect on the track's torsional vibration, so a curved beam model is needed to study the curved track's dynamic responses. © 2018, Editorial Office of Journal of Vibration and Shock. All right reserved.