Railway track dynamics with periodically varying stiffness and damping in the Winkler foundation

Abstract

We investigate the dynamics of the train/track system in case of an inhomogeneous longitudinal subgrade stiffness/damping distribution varying periodically along the track. In our study the track is modelled by a Bernoulli-Euler beam laying on a Winkler foundation of stiffness/damping parameters represented by continuous periodic functions. The damped oscillatory load is moving along the track at a constant velocity. In order to obtain an analytical solution to the boundary problem we utilize our previous method for the compactly supported case, based on the approximation of the parameter functions by generalized functions. A finite closed-form formula can be obtained with the help of principal values in the sense of Cauchy.