Calculation of dynamic responses of railway sleepers on a nonlinear foundation

The safety of a passing train depends on different factors, of which one of the most important is the behavior of the foundation. Therefore, the effects of the nonlinearity of ballast on the dynamic responses of the railway track are a key research interest. In this paper, a new model of railway sleepers posed on a nonlinear foundation has been developed. By coupling the finite element method (FEM) of the sleeper with an analytical model of the periodically supported beam model, the dynamic equation of the sleeper is developed. On the other hand, by considering a periodic series of moving loads, this equation can be transformed to a forced nonlinear oscillation. Iteration procedures have been built to calculate the periodic solution. This method has demonstrated a good convergence of results by comparison with the analytical solution in the linear case. The influence of the nonlinear foundation has been investigated by two examples: cubic-nonlinear and bi-linear foundations. The parametric studies demonstrate that numerical results converge with a small number of iterations.