A comparison of beam models for the dynamics of railway sleepers

In dynamics models for the railway tracks, the rails are considered as beams supported continuously or periodically mass-spring systems. Recently, the mass-spring systems are replaced by Euler-Bernoulli beams on viscoelastic foundation in order to study the dynamics of sleepers. This paper presents a development of this study by considering the Timoshenko beams for sleepers. We consider the dynamic equation in the steady-state of a sleeper subjected to the reaction forces. The rails are modelled by the periodically supported beams subjected to moving loads, leading to a relation between the sleeper displacements and the reaction forces. By substituting this relation into the dynamic equation, the sleeper responses can be obtained by using the Green’s function. Finally, numerical examples show the influences of beam models on sleeper responses. This development completes analytical choices for the dynamics of railway tracks where the rails and sleepers can be modelled by the two beam theories.