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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
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
GrowthпјљEuler<Timoshenko beams
ConvergenceпјљEuler>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
Result & Discussion
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.
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.
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