Numerical experiments for mathematical models of railway track oscillations

Abstract

Abstract. Two mathematical models of railway track oscillations are compared on the basis of numerical experiments. Introduction.Good mathematical models describing vibrations of railway track and trains are important and helpful in engineering studies concerning comfort and safety of travel (see [1]-[5]). The main goal of this work is a mathematical description of the dynamical behaviour of the system train-track. We present a numerical experiment for two different mathematical models of railway track oscillations. We consider only one-dimensional models. The first is based on Mathews' problem (see [2]), which treated a Bernoulli-Euler beam on an elastic foundation as an infinite rail track under the action of a moving (with velocity v) and harmonically oscillating force. The force of frequency /2π is vertical to the beam and at the point x and time t > 0 has the value F 0 cos t · δ(x − vt), where F 0 is the amplitude. In this model we do not take into account vibrations of the particular sleepers, but we introduce an elasticity term for the whole beam. The second model (see [4]) consists of an equation of a continuous Euler-Bernoulli beam and a differential equation describing vibrations of the sleepers. The track is considered as a system consisting of an infinite continuous elastic beam connected with a finite number of discrete masses modelling the sleepers. We imitate the motion of the train by the vertical force acting at one fixed point x = l and having the form F 0 e − ωt cos t · δ(x − l). The positive parameter ω is a substitute for the velocity of the train. Using realistic data we compare results of numerical experiments for both models.