Modelling and Simulation of a bridge interacting with a moving vehicle system

Abstract: The problem about the vibration of vehicles and bridge is mainly the problem of coupling vibration between the vehicles dynamic system and bridge dynamic system. The vehicles running on the bridge at some speed can make the bridge vibrate, at the same time the vibration of the bridge will also affect the vibration of the vehicles. This problem with interaction and mutual effects is the problem of coupling vibration between vehicles and bridge. Because its close relation to practical application it is paid extensive attention by more and more people. In this thesis we construct the kinetic model of the bridge subsystem and the vehicle subsystem separately. Then according to the Euler–Bernoulli beam theory, mode superposition method and D’Alambert principle we get the functions of the two models. In addition we refer to the relationship of the geometric on the contact point and the static equilibrium conditions to construct the relation between the equation of the vehicle vibration and the equation of bridge vibration. Finally we use MATLAB to write the code according to the Newmark-beta method to handle the coupled equation.