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Research Papers

# A Nonlinear Vehicle-Road Coupled Model for Dynamics Research

[+] Author and Article Information
Shaopu Yang

School of Mechanical Engineering,
Shijiazhuang Tiedao University,
Shijiazhuang, 050043, Hebei, PRC

Liqun Chen

Department of Mechanics,
Shanghai University,
Shanghai, 200444, PRC
e-mail:βlshsjz@163.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 15, 2010; final manuscript received April 15, 2012; published online July 23, 2012. Assoc. Editor: Nobuyuki Shimizu.

J. Comput. Nonlinear Dynam 8(2), 021001 (Jul 23, 2012) (14 pages) Paper No: CND-10-1091; doi: 10.1115/1.4006784 History: Received August 15, 2010; Revised April 15, 2012

## Abstract

This paper presents a nonlinear vehicle-road coupled model which is composed of a seven-degree of freedom (DOF) vehicle and a simply supported double-layer rectangular thin plate on a nonlinear viscoelastic foundation. The nonlinearity of suspension stiffness, suspension damping and tire stiffness is considered and the Leaderman constitutive relation and Burgers model are applied to describe the nonlinear and viscoelastic properties of the asphalt topping material. The equations of motion for the vehicle-road system are derived and the partial differential equation of road pavement is discretized into an infinite number of second-order ordinary differential equations and first-order ordinary differential equations by Galerkinβs method and a mathematic transform. A numerical integration method for solving this coupled system is developed and the nonlinear dynamic behaviors of the system are analyzed. In addition, the simulation results of the coupled model are compared to those of the uncoupled traditional model. It is found that with the increase of harmonic road surface roughness amplitude, the vehicle bodyβs vertical response is always periodic, whereas the pavementβs response varies from quasi-periodic motion to chaotic motion. In the case of a heavy-duty vehicle, a soft subgrade or a higher running speed, the application of the proposed nonlinear vehicle-road coupled model would bring higher computational accuracy and make it possible to design the vehicle and pavement simultaneously.

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## References

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## Figures

Fig. 1

Fig. 2

Burgers model

Fig. 3

Outer and internal forces of the pavement

Fig. 4

Numerical tests on time step Ξt and mode number NM

Fig. 5

Responses of vehicle body when Aβ=β0.002 m

Fig. 6

Responses of pavement when Aβ=β0.002 m

Fig. 7

Responses of pavement when Aβ=β0.02 m

Fig. 8

Responses of pavement when Aβ=β0.2 m

Fig. 9

The effect of nonlinearity on amplitude frequency responses

Fig. 10

Time histories of vehicle and pavement responses for linear and nonlinear system with fβ=β8.6 Hz

Fig. 11

The effect of viscoelastic characteristic on amplitude frequency responses

Fig. 12

Time histories of vehicle and pavement responses for elastic and viscoelastic asphalt topping with fβ=β8.6 Hz

Fig. 13

Responses comparison between coupled model and uncoupled model (Mβ=β15,280 kg, Vβ=β20 m/s, Aβ=β0.002 m, Kβ=β8βΓβ106 N/m3, ββcoupled, β-uncoupled)

Fig. 14

Forth power force comparison between coupled model and uncoupled model (Mβ=β15,280 kg, Vβ=β20 m/s, Aβ=β0.002 m, Kβ=β8βΓβ106 N/m3)

Fig. 15

Forth power force comparison between coupled model and uncoupled model with different group of parameters (ββcoupled, β-uncoupled) (a) Mβ=β15,280 kg, Vβ=β10 m/s, (b) Mβ=β15280 kg, Vβ=β10m/s, Aβ=β0.002 m, Kβ=β48βΓβ106 N/m3, Aβ=β0.002 m, Kβ=β8βΓβ106 N/m3, (c) Mβ=β21,260 kg, Vβ=β10 m/s, (d) Mβ=β15,280 kg, Vβ=β20 m/s, Aβ=β0.002 m, Kβ=β8βΓβ106 N/m3, Aβ=β0.02 m, Kβ=β8βΓβ106 N/m3

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