The effect of vertical-lateral coupling of rails including initial curvature

An understanding of the dynamic behaviour of railway tracks at high frequencies, in both vertical and lateral directions, is important for the assessment of rolling noise. Although many analytical models can be found in the literature, these mostly focus on the vertical vibration of the track. Studies of the lateral vibration are less common while the coupling between the vertical and lateral directions has received very little attention. In this paper, a model of a beam on an elastic foundation is introduced that accounts for the coupling of the vertical and lateral vibration behaviour. The model allows for the effects of beam curvature, asymmetry of the cross-section, shear deformation, rotary inertia and warping. Consideration is given to the fact that the loads at the rail head, as well as those exerted by the railpads at the rail foot, may not be applied through the centroid of the section. The track is subjected to a non-moving harmonic load and the solution is obtained in the wavenumber domain using the Fourier transform method. Results are presented as dispersion curves for the free rail and are validated with the aid of a Finite Element software. Closed form analytical expressions are derived, using contour integration, for the forced response. The track vibration decay rates are also presented and analysed as a means of assessing the noise performance of the rail and the influence of vertical-lateral coupling.