A Fast Analytic Method to Calculate the Dynamic Response of Railways Sleepers

Existing analytical models for railway tracks consider only one rail supported by a continuous foundation or periodic concentrated supports (called the periodically supported beam). This paper presents an analytical model for a railway track which includes two rails connected by sleepers. By considering the sleepers as Euler-Bernoulli beams resting on a Kelvin-Voigt foundation, we can obtain a dynamic equation for a sleeper subjected to the reaction forces of the rails. Then, by using the relation between the rail forces and displacements from the periodically supported beam model, we can calculate the sleeper responses with the help of Green's function. The numerical applications show that the sleeper is in flexion where the displacement at the middle of the sleeper is greater than those at the rail seats. Moreover, the deformed shape of the sleeper is nonsymmetric when the loads on the two rails are different. The model result agrees well with measurements performed using instrumented sleeper in situ.