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.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Mamlouk, M. S., 1997, “General Outlook of Pavement and Vehicle Dynamics,” J. Transp. Eng., 123(6), pp. 515–517. [CrossRef]
Cebon, D., 1988, “Theoretical Road Damage due to Dynamic Tyre Forces of Heavy Vehicles,” Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.), 202, pp. 103–117. [CrossRef]
Cebon, D., 1993, “Interaction between Heavy Vehicles and Roads,” SAE Paper No., 930001(SEA/SP-93/951).
Cole, D. J., 1996, “Truck Suspension Design to Minimize Road Damage,” Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.), 210(D), pp. 95–107. [CrossRef]
Kenis, W., 1992, “Heavy Vehicle Pavement Loading: A Comprehensive Testing Programme,” Heavy Vehicle and Road: Technology, Safety and Policy, Thomas Telford, London, pp. 260–265.
Sun, L., Cai, X., and YangJ., 2007, “Genetic Algorithm-Based Optimum Vehicle Suspension Design using Minimum Dynamic Pavement Load as a Design Criterion,” J. Sound Vib., 301, pp. 18–27. [CrossRef]
Stensson, A., Asplund, C., and KarlssonL., 1994, “Nonlinear Behaviour of a MacPherson Strut Wheel Suspension,” Veh. Syst. Dyn., 3(2), pp. 85–106. [CrossRef]
Zhao, H. P., 2001, “Dynamic Characteristics of Vehicle Suspension With Non-Linear Springs,” J. Mech. Strength, 23(2), pp. 165–167.
Zhu, Q., and Ishitobi, M., 2004, “Chaos and Bifurcations in a Nonlinear Vehicle Model,” J. Sound Vib., 275(3-5), pp. 1136–1146. [CrossRef]
Li, S. H., and Yang, S. P., 2004, “Investigation on Chaotic Motion in Hysteretic Nonlinear Suspension System With Multi-frequency Excitations,” Mech. Res. Commun., 31, pp. 229–236. [CrossRef]
Jia, Q. F., 2005, “Dynamic Characteristics of Bilinear Suspension System of Vehicle,” Eng. Mech., 25(1), pp. 88–92.
Georgios, T., Charles, W. S., and Emanuele, G., 2008, “Hybrid Balance Control of a Magnetorheological Truck Suspension,” J. Sound Vib., 317(3-5), pp. 514–536. [CrossRef]
Qiu, P., Wang, X. Z., and Ye, K. Y., 2003, “Bifurcation and Chaos of the Circular Plates on the Nonlinear Elastic Foundation,” Appl. Math. Mech., 24(8), pp. 779–784.
Yang, Z. A., Zhao, X. J., and Xi, X. Y., 2006, “Nonlinear Vibration and Singularities Analysis of a Thin Rectangular Plate on Nonlinear Elastic Foundation,” J. Vib. Shock, 25(5), pp. 69–73.
Xiao, Y. G., Fu, Y. M., and Zha, X. D., 2008, “Bifurcation and chaos of rectangular moderately thick cracked plates on an elastic foundation subjected to periodic load,” Chaos, Solitons and Fractals, 35(3), pp. 460–465. [CrossRef]
Zafir, Z., Siddharthan, R. V., and Sebaaly, P. E., 1994, “Dynamic Pavement Strain Histories from Moving Traffic Load,” ASCE J. Transp. Eng., 120(5), pp. 821–842. [CrossRef]
Siddharthan, R. V., Yao, J., and Sebaaly, P. E., 1998, “Pavement Strain from Moving Dynamic 3D load Distribution,” ASCE J. Transp. Eng., 124(6), pp. 557–566. [CrossRef]
Kim, D., Salgado, R., and Altschaeffl, A. G., 2005, “Effects of Supersingle Tire Loadings on Pavements,” ASCE J. Transp. Eng., 131, pp. 732–743. [CrossRef]
Mulungye, R. M., Owende, P. M. O., and Mellon, K., 2007, “Finite Element Modelling of Flexible Pavements on Soft Soil Subgrades,” Mater. Des., 28, pp. 739–756. [CrossRef]
Chen, J., 2002, A Basic Study on Interaction between Vehicle and Roadway [D], Jilin University, Changchun, P. R. C.
Ji, X. W., and Gao, Y. M., 1994, “The Dynamic Stiffness and Damping Characteristics of the Tire,” Automot. Eng., 5, pp. 315–321.
Xu, B., Shi, Y. B., and Wang, G. D., 2005, “Suspension Non-linear Components Influence upon Ride Comfort and Road Friendliness,” Veh. Power Technol., 1, pp. 46–51.
Judycki, J., 1992, “Non-Linear Viscoelastic Behaviour of Conventional and Modeled Asphaltic Concrete under Creep,” Mater. Struct., 25, pp. 95–101. [CrossRef]
Ke, J. P., and Ding, P., 2004, “Study on the Stress Relaxation Performance of Asphalt Mixture,” Highw. Automot. Appl., 4, pp. 64–66.
Leaderman, H., 1962, “Large Longitudinal Retarded Elastic Defomation of Rubber-Like Network Polymers,” Trans. Soc. Rheol., 6, pp. 361–382. [CrossRef]
Chen, L. Q., and Cheng, C. J., “Instability of Nonlinear Viscoelastic Plates,” Appl. Math. Comput., 162, pp. 1453–1463. [CrossRef]
Monismith, C. L, 1962, “Viscoelastic Behavier of Asphalt Concrete Pavements,” Proceedings of the 1st International Conference on the structural Design of Asphalt Pavements 1962, Vo1. 1.
Marynowski, K., and Kapitaniak, T., 2002, “Kelvin-Voigt versus Burgers Internal Damping in Modeling of Axially Moving Viscoelastic Web,” Int. J. Nonlinear Mech., 37, pp. 1147–1161. [CrossRef]
Cao, Z. Y., 2006, “Nonlinear Dynamic Analysis of Functionally Graded Material Plates,” Acta Mech. Solida Sinica, 27(1), pp. 21–25.
Cao, Z. Y., 1989, Vibration Theory of Plates and Shells [M], China Railway Press, Beijing.
Yang, S. P., Li, S. H., and Lu, Y. J., 2010, “Investigation on Dynamical Interaction between a Heavy Vehicle and Road Pavement,” Veh. Syst. Dyn., 48(8), pp. 923–944. [CrossRef]
Potapov, V. D., and Marasanov, A. Y., 1997, “The Investigation of the Stability of Elastic and Viscoelastic Rods under a Stochastic Excitation,” Int. J. Solids Struct., 34(11), pp. 1367–1377. [CrossRef]
Zhai, W. M., 2002, Vehicle-Track Coupling Dynamics, China Railway Publishing house, Beijing.
Zhai, W. M., 1996, “Two Simple Fast Integration Methods for Large-Scale Dynamic Problems in Engineering,” Int. J. Numer. Methods Eng., 39, pp. 4199–4214. [CrossRef]
GB/T7031-2005, Mechanical Vibration Road Surface Profiles Reporting of Measured Data.
ISO 2631-1978, Guide for the Evaluation of Human Exposure to Whole-Body Vibration.
Hu, H. Y., 2000, Applied Nonlinear Dynamics, Aero Industrial Press, Beijing.
Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A., 1985, “Determining Lyapunov Exponents from a Time Series,” Physica D, 16, pp. 285–317. [CrossRef]


Grahic Jump Location
Fig. 1

The nonlinear vehicle-road coupled system

Grahic Jump Location
Fig. 3

Outer and internal forces of the pavement

Grahic Jump Location
Fig. 4

Numerical tests on time step Δt and mode number NM

Grahic Jump Location
Fig. 5

Responses of vehicle body when A = 0.002 m

Grahic Jump Location
Fig. 6

Responses of pavement when A = 0.002 m

Grahic Jump Location
Fig. 7

Responses of pavement when A = 0.02 m

Grahic Jump Location
Fig. 8

Responses of pavement when A = 0.2 m

Grahic Jump Location
Fig. 9

The effect of nonlinearity on amplitude frequency responses

Grahic Jump Location
Fig. 10

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

Grahic Jump Location
Fig. 11

The effect of viscoelastic characteristic on amplitude frequency responses

Grahic Jump Location
Fig. 12

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

Grahic Jump Location
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)

Grahic Jump Location
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)

Grahic Jump Location
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




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In