A three-dimensional modal theory-based Timoshenko finite length beam model for train-track dynamic analysis

An efficient Timoshenko beam model of finite length is developed for train-track interaction dynamics. The rail is reduced to the present beam model and its vertical and lateral bending, shear, and torsion deformations are considered. A moving control volume attached to the train is introduced, which encloses the reduced rail, and a reference coordinate system is established in the reduced rail at the left end. The arbitrary Lagrangian-Eulerian (ALE) method and the modal superposition method (MSM) are adopted, and governing equations of the reduced rail model are derived by Lagrange's equations. Owing to the advantages of the MSM, the number of degrees of freedom of the current formulation is clearly reduced and its efficiency is greatly improved. A long non-ballasted track of finite length subjected to a constant moving load is first considered, and results from the present beam model are in good agreement with those from the traditional finite element method. A three-dimensional train-track interaction problem with consideration of a ballasted track is further studied. Results from the present beam model are compared with those from the commercial software Simpack where the MSM is used, and they are in good agreement with each other. Since the number of modes in the present beam model is much fewer than that in Simpack, the present beam model is more efficient than that in Simpack. It is found that the number of shape functions and the length of the beam model used in calculation can significantly affect the accuracy and efficiency of the present beam model, which should be taken into consideration. The current beam formulation is independent of the moving velocity of the train and can handle train-track dynamics with variable train velocities. The current beam formulation is straightforward and can be easily extended in various complex applications. It is more suitable for dealing with long-term train-track interaction dynamics. (C) 2020 Elsevier Ltd. All rights reserved.