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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: 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

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 Galerkin’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 body’s vertical response is always periodic, whereas the pavement’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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Figures

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Fig. 1

The nonlinear vehicle-road coupled system

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Fig. 3

Outer and internal forces of the pavement

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Fig. 4

Numerical tests on time step Δt and mode number NM

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Fig. 5

Responses of vehicle body when A = 0.002 m

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Fig. 6

Responses of pavement when A = 0.002 m

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Fig. 7

Responses of pavement when A = 0.02 m

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Fig. 8

Responses of pavement when A = 0.2 m

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Fig. 9

The effect of nonlinearity on amplitude frequency responses

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Fig. 10

Time histories of vehicle and pavement responses for linear and nonlinear system with f = 8.6 Hz

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Fig. 11

The effect of viscoelastic characteristic on amplitude frequency responses

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Fig. 12

Time histories of vehicle and pavement responses for elastic and viscoelastic asphalt topping with f = 8.6 Hz

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Fig. 13

Responses comparison between coupled model and uncoupled model (M = 15,280 kg, V = 20 m/s, A = 0.002 m, K = 8 × 106 N/m3, ——coupled, —-uncoupled)

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Fig. 14

Forth power force comparison between coupled model and uncoupled model (M = 15,280 kg, V = 20 m/s, A = 0.002 m, K = 8 × 106 N/m3)

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Fig. 15

Forth power force comparison between coupled model and uncoupled model with different group of parameters (——coupled, —-uncoupled) (a) M = 15,280 kg, V = 10 m/s, (b) M = 15280 kg, V = 10m/s, A = 0.002 m, K = 48 × 106 N/m3, A = 0.002 m, K = 8 × 106 N/m3, (c) M = 21,260 kg, V = 10 m/s, (d) M = 15,280 kg, V = 20 m/s, A = 0.002 m, K = 8 × 106 N/m3, A = 0.02 m, K = 8 × 106 N/m3

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