Timoshenko beam finite element for vehicle—track vibration analysis and its application to jointed railway track

A Timoshenko beam finite element suitable for vehicle-track vibration analysis is proposed and is applied to a jointed railway track. In several simulation models, the track vibration excited by a train running on the rail is formulated as a dynamic problem where a sequence of concentrated loads moves on the discretely supported Timoshenko beam. The external force is then defined by the concentrated load. The Timoshenko beam subjected to concentrated loads deforms with the slope discontinuity at the loading points. This deformation cannot be represented by the usual finite elements, which causes the fictitious responses of the beam. The present finite element model removes the undesirable response by completely modelling the slope discontinuity. This is achieved by the TIM7 element with the piecewise-linear hat functions. The jointed track model constructed by this finite element is employed to predict the impulsive wheel—track contact force excited by the wheel passage on rail joints. The rail joints with fishplates are of great concern to track deterioration, the settlement of ballast track and the failure of track components. In the present paper the effects of train speed and gap size of the joints on the impact force are assessed from simulation results.