Sliding window method for vehicles moving on a long track

The rail is modelled as a simply supported beam in the vehicle–track coupled dynamics. The beam is formulated by a partial differential equation that is transformed into an ordinary differential equation by the method of mode superposition for numerical calculation. However, the size of the matrix that is formed by the mode-superposition method increases significantly with track length, which limits the calculation efficiency. Some methods have been developed to solve this calculation issue, but they diminish the merits of the vehicle–track coupled dynamics, which would systematically investigate the dynamics of a vehicle and a track from the entire vehicle–track system. A new method is developed to resolve this contradiction. First, a theory based on a sliding window is established to improve the computational stability with respect to the length and the window-movement ratio. Then, two methods, namely finite element method analysis and an analytical solution, are used to verify the accuracy of the new method, which is highly efficient when used in a vertical half-vehicle–track coupled model to calculate the vehicle response when the vehicle moves on a long track. The results of the vehicle response calculated with and without the sliding window show good consistency.