Assessment of numerical integration algorithms for nonlinear vibration of railway vehicles

The primary purpose of this paper was to choose appropriate time integration methods for the simulation of nonlinear railway vehicle systems. The nonlinear elements existing in railway vehicle systems were summarized, and the relevant mathematical expressions were provided. A newly developed integration method, which is the corrected explicit method of double time steps, was implemented in five typical nonlinear examples of nonlinear railway vehicle systems. The Newmark method, the Wilson-θ method, the Runge–Kutta method, the predictor-corrector Adams method, the Zhai method, and the precise integration method were also employed for comparison purpose. Finally, the scope of application of these methods was pointed out . The results show that the Newmark method and the Wilson-θ method should not be applied to nonlinear railway vehicle systems as these methods result in errors. In contrast to the predictor-corrector Adams method and the precise integration method, the Runge–Kutta method with error control (...