Global Bifurcation Analysis of a Nonlinear Road Vehicle System

[+] Author and Article Information
Zhaoheng Liu1

Department of Mechanical Engineering, École de Technologie Supérieure,  Université du Québec, Montreal, Quebec, H3C 1K3, Canadazhaoheng.liu@etsmtl.ca

Guy Payre

Department of Mechanical Engineering,  Université de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Canadaguy.payre@usherbrooke.ca


Corresponding author.

J. Comput. Nonlinear Dynam 2(4), 308-315 (Apr 05, 2007) (8 pages) doi:10.1115/1.2754307 History: Received November 16, 2005; Revised April 05, 2007

This paper investigates the global stability behavior present near a bifurcation point of a nonlinear road vehicle system. The nonlinear behavior of the system is determined by reducing its dimensions according to the center manifold theory applied to a nongeneric case. A generalized Hopf bifurcation is analyzed by unfolding the limit cycle mean amplitude equation into a two-parameter space. The numerical application of the analytical framework demonstrates the coexistence of two limit cycles for certain ranges of physical and driver parameter values.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 2

Unfolding directions (ε1,ε2) in the plane (μ1,μ2)

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Figure 3

Bifurcation diagram for μ2=−0.01

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Figure 4

Bifurcation diagram for μ2=0

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Figure 5

Bifurcation diagram for μ2=0.02

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Figure 6

Time histories of limit cycle and asymptotic stable motions for μ2=0.02



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