§16§The main objective of this book is to establish efficient numerical models within the framework of finite element method to solve the dynamic response of the Vehicle-Bridge Interaction (VBI) systems for vehicles moving with constant velocity or with acceleration. For vehicles with constant velocity, the dynamic condensation method is applied to reduce the vehicle DOFs to the VBI element. VBI element refers to bridge beam elements that are in direct contact with wheels of the vehicles traversing the bridge. A new formulation is proposed for the mass, damping, and stiffness of the VBI element considering new formulation for the contact points. For vehicles experiencing sudden deceleration with sliding, external forces resulting from vehicle horizontal deceleration are numerically formulated in a matrix form as the function of vertical contact forces. By defining a new parameter called acceleration parameter with particular characteristics, the contact force formula is reformulated. §16§Consequently, a new formulation for the VBI element containing the effect of vehicle acceleration is developed.
