Solving for railway deformations using Weeks' method and undetermined coefficients

Abstract

With the increasing demands being placed on railway infrastructure, we are motivated to provide readily accessible solutions to models which can be used to describe the mechanics of rail track, particularly at transition zones. Transition zones, where foundation materials change abruptly along the track, are of particular interest as they have to be maintained as much as eight times more frequently than standard track sections. Modelling the railway as an infinite Euler–Bernoulli beam on a viscoelastic foundation, we apply the Laplace transform to eliminate time derivatives and solve the resultant ordinary differential equation in space by the method of undetermined coefficients. The
Laplace transform must then be inverted by a numerical technique, to which end we provide a practical description of Weeks’ method. The results obtained through the application of this method are compared to published solutions for the steady-state deformation of rail track at transition zones.

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