Calculation of Dynamic Responses of a Cracked Beam on Visco-Elastic Foundation Subjected to Moving Loads, and its Application to a Railway Track Model

Abstract

In this study, the dynamic responses of a cracked beam layed on a visco-elastic foundation subjected to moving loads are calculated. An Euler–Bernoulli beam model is used to describe the beam behaviors. In addition, the beam has several open cracks one-sided with different depths. By using the Fourier transform, the dynamic responses of the beam are determined analytically in the frequency domain with the help of Green’s function. By coupling with the periodic supported beam model, an analytical model of the railway sleeper is developed. This model allows the fast calculation of the dynamic responses of a damaged sleeper. A dynamic computational model using the FEM method was also developed and compared to the analytical model. The results from the two methods are relatively comparable for three cases of beams without cracks, beams with one crack, and beams with two cracks.