Vehicle-Bridge Interaction Analysis By The Symplectic Method

The dynamic properties of the bridge are involved in the dynamic responses of the vehicle and bridge when they interacted with each other and can be extracted to monitor its health conditions. In this work, the vehicle is simplified as a system of spring-damper-mass while the bridge as a Timoshenko beam. The coupled governing equations of the vehicle-bridge interaction are derived, then the governing equation of the beam is written in state space formulation and the orthogonality property of the modal displacements is proved. Taking advantage of the mode orthogonality, vehicle-bridge interaction equation is decoupled, and the responses of vehicle and bridge are obtained by iteration procedure then. Due to adopting state space formulation, the method can be applied to beam with varying section and multi-span beam, and more complicated factors can be taken into account, such as harmonic load on vehicle, noise interference in measurement of vehicle acceleration signal and road surface roughness. Some numerical examples are given, which demonstrate the validity of this method, and the effects such as damping of bridge, damping of vehicle, the vehicle to bridge mass ratio, harmonic load on vehicle, white Gaussian noise interference and road surface roughness are taken into account in further research of identifying bridge fundamental frequency from the dynamic response of a passing vehicle. Moreover, formulas the vehicle-bridge vibration of analytical solutions of three-span bridge are partly deduced.