High efficient dynamic analysis of vehicle–track–subgrade vertical interaction based on Green function method

A new method is proposed to efficiently simulate vehicle-track-subgrade vertical dynamic interactions based on the Green function method. In this simulation, the vehicle-track-subgrade system is divided into two subsystems, the vehicle-rail subsystem and the slab-subgrade subsystem, which are coupled through fastener connections. In the vehicle-rail subsystem, the vehicle is modelled as a multi-rigid-body system with 10 degrees of freedom, and the rail is simplified as a Bernoulli-Euler beam supported by rail pads. Dynamic equations of the vehicle-rail subsystem are described by differential equations. In the slab-subgrade subsystem, a three-dimensional finite element model is established to obtain the Green functions of the system induced by a unit impulse excitation. Based on the derived Green functions, dynamic equations of the slab-subgrade subsystem are formulated by the Duhamel integral. The interaction between the two subsystems is transferred by the fastener forces, and the dynamic responses of the whole system are solved through explicit numerical methods. The proposed method is subsequently validated through a detailed numerical comparison with the result obtained by the finite element method. Finally, the method is applied to investigate the dynamic property of the subgrade system under high-speed train operation.