A vehicle-track-bridge interaction element considering vehicle's pitching effect

A finite element method is applied to analyze the dynamic responses of railway track and bridge under a moving railway vehicle. The vehicle, track and bridge are regarded as an integrated system. The moving vehicle is modeled as a two-axle mass-spring-damper system having four degrees of freedom. The rails and the bridge deck are modeled as an elastic Bernoulli-Euler upper beam with finite length and a simply supported Bernoulli-Euler lower beam, respectively, while the elasticity and damping properties of the rail bed are represented by continuous springs and dampers. A vehicle-track-bridge interaction element considering vehicle's pitching effect is proposed for studying the interactions among moving vehicles, and its supporting railway track structure and bridge structure. The element consists of a vehicle modeled as a two-axle mass-spring-damper system having four degrees of freedom, two upper beam elements to model the rails, two lower beam elements to model the bridge deck, and continuous springs and dampers to model the rail bed between two upper beam elements and two lower beam elements. The equations of motion for the vehicle-track-bridge interaction element are directly derived by means of Hamilton principle. After by assembling the stiffness matrices, the damping matrices, the mass matrices and the vectors of nodal loads of all elements, the global equations of motion for the integrated system are obtained. These equations are solved by step-by-step integration method, to obtain simultaneously the dynamic responses of vehicle, track and bridge. Several illustration examples are presented.