Dynamic response of a curved railway track subjected to harmonic loads based on the periodic structure theory

In this study, the authors have analysed the dynamic response of a curved railway track that is subjected to moving and non-moving harmonic loads. The track is considered as a curved Timoshenko beam supported by periodically spaced discrete fasteners. The displacement and rotation of the curved rail are expressed as the superposition of track modes in the frequency domain. Periodic structure theory is applied to the equations of motion of the curved track, allowing the dynamic response of the track to be calculated efficiently in a reference cell. The effect of the stiffness and damping of the fasteners, the fastener spacing and the radius of curvature on the mobility and decay rate of the track are analysed for non-moving loads on the rail head. The vibration of the rail due to moving loads is also discussed. It is found that the dynamic response of a curved rail with a large radius has the same characteristics as that of a straight track. However, the dynamic response of the track is significantly affected when the radius of curvature becomes small. The radius affects the mobility; it also has an effect on the track decay rate below 2000 Hz and the velocity of the rail in the vertical direction when the radius is smaller than about 15 m and for the lateral direction when it is less than about 30 m. Moreover, the curvature has a significant influence on the vertical/lateral cross mobility, the magnitude of which increases as the radius is reduced. When the radius is larger than 10m, the amplitude of the lateral vibration under a moving vertical load and the vertical response to a moving lateral load are inversely proportional to the radius.