Modeling and dynamic analysis method of vehicle-bridge coupling system considering car-body flexibility

The car-body of a railway vehicle is flexible in nature.Car-body flexibility is considered while the wheel-sets and the bogies of a railway vehicle are regarded as rigid bodies in the proposed vehicle-bridge dynamic interaction analysis method.The vehicle is considered as a spatial structure supported on the wheel-rail interface through Hertz nonlinear spring.The wheel-sets and bogies are established by rigid beam elements coded in general finite element software.The car-body is modeled by flexible beam elements,and linear stiffness of the primary and the secondary suspensions is modeled by spring elements in the same software.The damping forces of the suspensions and the wheel-rail interaction forces on wheel-sets are treated as pseudo forces acted on the vehicle subsystem.The wheel-rail interaction forces on the rails are similarly treated as pseudo forces acted on the bridge subsystem.Mode analyses are conducted based on finite element models of the vehicle and the bridge.And then mode superposition method associated with pseudo force treatment is applied to establish equations of motion of the coupling vehicle-bridge system.An iterative scheme is used to solve the equations of the system.The proposed method is firstly verified by a numerical example,and then the vibration of the car-body with different flexibility is numerically simulated when high speed train traverses multi-span simply supported bridges.The car-body acceleration is found to be underestimated if its flexibility is not considered,especially when flexible car-body resonance phenomena occur.Nevertheless,the bridge acceleration is hardly affected by flexible car-body vibration.