A hybrid solution for studying vibrations of coupled train–track–bridge system

This article develops a hybrid model to analyse the dynamic interactions between a train, tracks and a bridge. The model couples the train and track subsystems to form an integrated time-dependent subsystem through a vertically interacting wheel–rail model. In turn, this time-dependent subsystem is coupled with the bridge subsystem by enforcing the compatibility of forces at the contact points between the track and the bridge. A new hybrid solution algorithm is proposed which combines the strongly coupled method and the loosely coupled method to numerically solve the equation of motion of the coupled train–track–bridge system in the time domain. The integrated time-dependent equation of motion of the train–track subsystem is solved by applying the strongly coupled method. The equilibrium equations of the train–track subsystem and bridge subsystem are then solved via the loosely coupled method using the Newmark integration scheme. Significantly faster convergence can be achieved by avoiding the iterative equilibrium calculations between the wheel and the rail, and the total computational efficiency increases significantly because of the considerably smaller size of the time-dependent equations of motion and larger integration time step. The accuracy and computational cost of the proposed method are validated and compared to the existing models using a case study on the vibration of a cable-stayed bridge.