A fast random method for three-dimensional analysis of train-track-soil dynamic interaction

A fast computation method that can be used for efficient analysis of full scale three-dimensional random vibrations induced by railway traffic is presented in this paper. The method uses the pseudo-excitation method (PEM) for random analysis and the proposed multi-point synchronous algorithm (MPSA) for solution of the large sparse linear equations of the train-track-soil coupled system (TTSCS). A mixed two- and three-dimensional TTSCS model is established firstly. Based on the linear Hertzian wheel/rail contact relationship, the time-dependent equations of motion of the TTSCS are deduced. This formulation leads to a global system of equations that can be solved in a directional manner without the need for iterative processes. By means of the PEM, the self-excitation induced by the random track irregularity is transformed into a series of deterministic harmonic excitation vectors. To accelerate the computation, a fast computation strategy is proposed. In the numerical example, the proposed method is validated through comparison with field measured results. Comparison of the results of the MPSA with those of the triangular factorization algorithm and ANSYS is undertaken to evaluate the efficiency of the MPSA. It is confirmed that the MPSA can result in a five- to tenfold increase in computation efficiency.