Comparative analysis of beam models for vertical rail vibrations under dynamic forces

An analytical model of the rails of ballasted railway track subjected to the dynamic loads are developed to study forced vertical vibration. In this work, the two rails are modelled as infinite uniform beams posed on a system of periodical supports with the help of Timoshenko beam theory. Besides, each support is considered as a beam posed on a visco-elastic foundation. A linear relation between the sleeper displacement at the crossing-points with two rails and the two reaction forces is established via the Green’s function in the frequency domain. In other words, the mechanical behaviour of the support can be written as a spring with an equivalent stiffness. By replacing this relation into the periodically supported rail models, the forced vertical vibrations of two rails are obtained analytically. This analytical model allows calculate rapidly the rail responses in different load, especially in the non-symmetric configuration. In addition, the comparison of rail responses calculated by two beam models are investigated. This work concerns the study of peaks resonances of the frequency responses functions which is useful to understand the excitations of rolling noise.