Analytical modelling of the vibration of railway track

The high frequency dynamic behaviour of railway track, in both vertical and lateral directions, strongly affects the generation of rolling noise as well as other phenomena such as rail corrugation. One aspect that has received little attention is the coupling between the vertical and lateral directions. This thesis sets out to build an analytical model of a railway track with three principal targets: to improve the modelling for lateral vibration compared with existing models, to identify the most important sources of coupling between the vertical and lateral directions and to quantify the implications for rolling noise phenomena.Simple models for the axial, torsional, vertical and lateral vibrations of beams are first introduced. The results from these models are analysed based on their dispersion curves and their characteristic behaviour is identified. Furthermore, effects of cross-section asymmetry, shear deformation, rotational inertia, restrained warping and curvature are considered, as well as the fact that the loads at the rail head do not always act through the centroid of the rail section. These beam models are then brought together to formulate a fully coupled beam model.An elastic foundation is then introduced to the beam model to represent the railpads and the dispersion characteristics of the whole track are discussed. Subsequently, the effect of the foundation location is investigated, as well as the inclusion of additional layers of masses and springs, representing the sleepers and ballast. Two different sleeper models are introduced. The first is that of a simple mass allowed to translate and rotate, representing a single block of a bibloc sleeper. The second is that of a flexible finite length beam accounting for vertical, lateral, axial and torsional vibration, representing a monobloc sleeper, which is more widely used in railway tracks. The response of the beam model is compared against measurements performed on sleepers in the laboratory. An average error of less that 1% is observed for the natural frequency of all modes, excluding the first mode. This mode is most influenced by the sleeper cross-section variation which is not directly accounted for in the model