Nonlinear Vibration of Vehicle-pavement Coupled System Based on High-order Galerkin Truncation Yan Yang, Hu Ding, Li-qun Chen Shanghai institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China Abstract In this dissertation, the vehicle model, pavement model and foundation model are linked by the road surface roughness. Based this coupled system, the nonlinear partial differential governing equations of the vehicle-pavement coupled vibration are developed. The dynamic response of coupled system is solved using the high-order Galerkin truncation method in conjunction with Runge-Kutta method. The effects of different truncation terms on the dynamical responses of the vehicle-pavement nonlinear vibration are discussed, and the convergence of the Galerkin truncation to investigate the vehicle-pavement coupled vibration are determined for the first time. Engineering Background & Mathematica Model Fig.4. Comparison between the different beam theories of the pavement: (a) the natural frequencies versus terms; (b) the vertical displacements of the pavement’s midpoint versus truncation terms Growth：Euler<Timoshenko beams Convergence：Euler>Timoshenko beams Response: Euler>Timoshenko beams 2.Coupling Effect Fig.1. Engineering model of pavement Fig.2. Schematic representation of a Timoshenko beam subjected to two-DOF moving oscillator on a nonlinear viscoelastic Pasternak foundation Fig.5. Effects of the speed of the vehicle: (a) on the biggest displacement of the vehicle body; (b) on the biggest vertical displacement of the pavement’s midpoint Result & Discussion The vertical deflections of the pavement's midpoint and the vehicle body are completely opposite. 1.Convergence Studies 3.Physical parameter Studies Fig.3. Convergence of the Galerkin truncation method: (a) on the vertical displacement of the beam’s midpoint; (b) on the vertical displacement of the vehicle body Fig.6. Effects of the linear elastic modulus of the subgrade: (a) on the vertical displacement of the pavement’s midpoint; (b) on the motion of the vehicle body The coupled vibratory response needs high-order modes. The pavement is affected more than the vehicle.