Nonlinear Vibration of Vehicle-pavement Coupled System Based on High-order Galerkin Truncation

1. 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 Key Laboratory of Mechanics in Energy Engineering Shanghai University, Shanghai 200072, P.R. of China E-mail address: dinghu3@shu.edu.cn (H. Ding) Introduction Growth：Euler<Timoshenko beams Convergence：Euler>Timoshenko beams Response: Euler>Timoshenko beams 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. 2.Coupling Effect Fig.1. Engineering background 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. Mathematical Model 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 The vertical deflections of the pavement's midpoint and the vehicle body are completely opposite. 3.Physical parameter Studies Fig.2. Schematic representation of a Timoshenko beam subjected to two-DOF moving oscillator on a nonlinear viscoelastic Pasternak foundation Result & Discussion 1.Convergence Studies 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 pavement is affected more than the vehicle. Conclusion 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 1.The 100–term Galerkin truncation for the dynamic response of the system yields rather accurate results. 2.The motion of the pavement and the vibration of the vehicle are coupled. The coupled vibratory response needs high-order modes. Acknowledgement The authors gratefully thank Mr. *** for his contributions to improve the writing of this paper. The authors gratefully acknowledge the support of the State Key Program of National Natural Science Foundation of China through Grant Nos. 10932006 and 11232009, and Innovation Program of Shanghai Municipal Education Commission through Grant No. 12YZ028. 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