Numerical Methods For The Dynamic Interaction And Multi-Support Seismic Response Of Vehicle-Bridge Coupled Systems

Vehicle-bridge coupled systems are complex time-dependent dynamic systems. With the continuous increase of the vehicle’s speed, weight and traffic density, the dynamic characteristics and vibration control of the vehicle-bridge coupled systems have received more and more attentions. In addition, with the rapid development of highways and high-speed railways, bridges are widely used and the probability of the vehicle running over a bridge while earthquake occurs has considerably increased. Furthmore, the possibility of separations between the moving objects and the bridge and the randomness road/track irregularity makes the coupled system become more sensitive to the inhomogeneous and non-stationary random ground motions due to high flexibility and low damping of the bridge.There are two conventional ways to simulate the time-dependent equations of motion of vehicles-bridge systems. The first one is based on the uncoupled iteration method, in which each system (both the vehicles and the bridge) is solved separately and an iterative process in each time step is performed to find the equilibrium between the bridge and vehicle wheels. The other way to simulate the dynamic interaction between the vehicle and bridge consists of solving the whole fully coupled system, and the solution is given at each time step without any iteration in the time step. The principal advantage of the iterative method is that both the vehicle and the bridge can be treated by using the traditional dynamic method, in addition, the ill-conditioned matrices due to considerable different parameter values in the time-variant method are avoided, and it requires a smaller time step than the previous one.Based on the iterative method of vehicle-bridge coupled systems, a non-iterative approach is proposed by predicting the interaction forces between the vehicle and bridge. The present method is more efficient than the traditional iterativemthod, and has similar precision. The equations of motion of the vehicle and bridge are solved independently and the iterative process is not necessary anymore. The transfer mode of interaction forces between the vehicle and bridge is studied, and a linear complementarity method for a vehicle-bridge dynamic system considering separation and random roughness is established. Furthermore, an efficient method for the non-stationary seismic response analysis of vehicle-bridge coupled systems with multiple input ground motions is proposed. The detailed studies can be summarized as:1) Based on the finite-element (FE) method and Duhamel integration, a numerical-analytical combined method for the problem of dynamic response of a FE bridge under moving loads is proposed, and the conditions of resonance and cancellation for the bridge subjected to multiple moving loads are derived. The FE modes of the whole structure are first computed and then converted into an analytical form that is constructed over all the elements of the top deck of the bridge through the element shape functions. The analytical dynamic responses of the bridge are derived from Duhamel integration, and transformed into a simple integration and a summation of the previous results through elimination of the time variable from the integration, which makes the computation process more efficient. Moreover, the conditions of resonance and cancellation for the bridge subjected to multiple moving loads are derived explicitly.2) A non-iterative method is proposed based on a prediction of the interaction forces between the vehicle and bridge, which can considerably reduce the computational effort without significant loss of precision. It is shown that the present interaction forces between the vehicle and bridge can be predicted for both linear and non-linear connections. The vehicle and bridge can be treated separately and directly by using the precise integration method, in which the complicated and time-consuming iterative process in the traditional iterative method is avoided. A similar precision may be achieved for considerably less effort.3) A linear complementarity method for a vehicle-bridge dynamic system considering separation and random roughness is established. By introducing the linear complementarity relationship between the relative displacement of the wheels and the bridge at the contact points, the dynamic interaction problem of the vehicle-bridge coupled system is transformed into a standard linear complementarity problem, and two models with different connection relations between the wheels and the bridge are proposed. The presented models characterize the system with one unified formulation whether the wheels separate from the bridge or not, and the conventional trial-and-error iterative process in numerical simulation is avoided.4) A method for the non-stationary random responses of vehicle-bridge coupled systems is presented under both stationary track irregularities and non-stationary multiple input earthquake excitations. Random seismic responses of a3D train moving along a realistic long-span bridge due to the wave passage, incoherence and site-response effects are extensively investigated. Further discusses of non-stationary random responses of vehicle-bridge coupled systems due to separation between wheels and bridge are fulfilled by using random vibration theory.