An uncoupled approach for vehicle bridge interaction analysis

A formulation of the coupled equations of motion for the bridge-vehicle dynamic interaction problem is proposed. This is derived through the Lagrange’s equation and adopts a compatibility condition at the interface bridge-vehicle, assuming that the two systems are always in contact. The pavement roughness can be considered in a simple way, through a roughness profile either generated from a PSD spectrum or based on experimental data. The coupled equations are forcibly uncoupled, moving the coupling terms to the RHS of the equations as forcing terms. The equilibrium condition at the interface, stated by the action-reaction principle, is then imposed through an iterative solution. Two iteration strategies are developed in the time domain; leaving generality to the iterative approach, separate and uncoupled mechanical models for the vehicle and the bridge are adopted. Both strategies consider: (a) a vehicle moving on the bridge at constant velocity along a straight direction, transmitting vertical contact forces to the bridge; (b) the sum of contributions from the bridge deflection and the pavement roughness as prescribed motion at the wheels of the vehicle. Procedure WTH iterates over the whole time-history and relies on a general purpose FE code for the structure; an ad hoc code has been developed for the vehicle. Thus, the bridge is subjected to the time history of contact forces, the vehicle is subjected to the time history of prescribed displacements and velocities. Convergence on contact forces involves the rms values during the whole time history. Procedure STS is implemented in an ad hoc developed code that needs the stiffness and mass matrix of the structure as input data. A two-phase iteration strategy within each time step is adopted; in the predicting phase the vehicle is moved to the step final position, in the correcting phase the forces transmitted by the vehicle are updated with the current values of the bridge displacement and velocities. The convergence check involves the variation of contact forces from an iteration to the next one. The first numerical studies are performed on a simply supported RC bridge, considering a 3D, 7DOFs vehicle model and two simpler 2D, 1 DOF and 4DOFs ones.