Abstract Summary
The serviceability of a high-speed railway track depends on the limitation of the dynamic amplifications that occur for load velocities near the critical one, that is, it depends on the ability of its substructure to dissipate the energy transmitted by the transit of the moving loads. This substructure is composed of many stones of several sizes and shapes, interacting according to the laws of unilateral and frictional contact mechanics. In (Toscano Corrêa, Pinto da Costa, Simões, Finite element modelling of a rail resting on a Winkler-Coulomb foundation and subjected to a moving concentrated load, International Journal of Mechanical Sciences, 140, 432-445, 2018), a new foundation model with a non-smooth character nearer to the true frictional dissipative character of the ballast was proposed. In that study a time stepping algorithm specially designed to deal with non-smooth dynamical systems was for the first time applied to distributed frictional foundations and new conclusions on critical velocities, maximal displacements and dynamic amplification factors were drawn. In this work a finite element program is developed to compute the steady state solution of an Euler-Bernoulli beam under a moving load, on a foundation composed of a continuous distribution of linear elastic springs associated in parallel with a continuous distribution of Coulomb frictional dampers. The motion of the beam is governed by a partial differential inclusion that is semi-discretized in space, using the finite element method, as a system of ordinary differential inclusions and integrated using a special implementation of the Non-smooth Dynamics Method (NSD) adapted to distributed Coulomb friction. The steady state solutions are then obtained for different values of the maximum force per unit length of the frictional dampers and for different values of the load velocity at both subcritical and supercritical regimes. The goal of this study is to generalize, for more realistic behaviours, the analyses in the literature so that it can be of interest in terms of engineering analysis of high-speed railway tracks.
