Hybrid solution of an infinite beam on a locally inhomogeneous and non-linear Winkler foundation excited by a constant moving load

Transition zones in railway tracks require a high maintenance frequency which leads to high costs and delays. To better understand the underlying mechanisms, a one-dimensional model is used, consisting of an infinite Euler-Bernoulli beam resting on locally inhomogeneous and non-linear viscoelastic Winkler foundation subjected to a constant moving load. The Winkler foundation is assumed to be piecewise linear, and the system thus behaves linearly between nonlinear events. Therefore, the solution can be obtained using a mixed time-frequency method. Using the Finite Difference Method for the spatial discretization combined with derived non-reflective boundary conditions enables us to simulate the behaviour of an infinite system. Results show that the plastic deformation in the transition zone is a consequence of constructive interference of the excited free waves and the eigenfield. The model presented here can be used for preliminary designs of transition zones in railway tracks, and also for preliminary predictions of the structure’s remaining life time.