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 University, Shanghai , 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.