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

Abstract

The dynamic response of a curved railway track subjected to moving and non-moving harmonic loads is studied in this paper. 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 a 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 is analysed for non-moving loads on the rail head. The vibration of the rail under 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, the 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 10 m, the lateral vibration amplitude under a moving vertical load and the vertical response to a moving lateral load are inversely proportional to the radius.

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ORCID for David Thompson: orcid.org/0000-0002-7964-5906

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