The nonlinear dynamical analysis of damaged concrete slab of high speed railway track using the revised Fourier pseudo-spectral method

Abstract

A revised Fourier pseudo-spectral method is applied to quickly solve the dynamic response of the railway ballastless track structure with damage. Considering the nonlinearity of the material damage of the track slab and the base, the pseudo-spectral method (PSM) of collocation format is used to discretize the vibration equation of the track slab and the base in spatial domain. Since the convergence and solution precision of the collocation method are greatly related to the collocation scheme, in order to ensure the quasi-convergence of the pseudo-spectral method, the Fourier-Galerkin spectral method is used to obtain the elastic convergence solution of the periodic dynamic model of the ballastless track, which is used as the criterion for quasi-convergence of the approximate solution of PSM. In order to reduce the number of collocation points and improve the accuracy of the approximate solution of PSM, the ballastless track model with discrete point support is replaced by the ballastless track model with uniformly continuous support. The optimal number of collocation points for the quasi-convergence of the PSM is obtained. Then, the interpolation basis function of the PSM is regularized, and the modified PSM is proposed, with which the model can achieve quasi-convergence under given collocation point number. In this paper, the accuracy of the pseudo-spectral method is improved, and the principle of collocation point selection is established, which makes it feasible for the nonlinear periodic spectral method to be applied to the damage evolution analysis, life prediction and structural dynamic optimization of the ballastless track.