Bifurcation analysis of nonlinear vehicle system under road excitation

A new hysteresis contact force model is proposed to simulate the vibration characteristics with road profile excitation. The dynamic characteristics, period doubling bifurcation, hardening type nonlinearity and the coexisting of periodic solutions are studied numerically with bifurcation map, phase portraits and basin of attractor. The cell mapping method is introduced to study the global characteristics of the quarter car vibrations. The quarter car model used in this paper is very simple and would not be sufficient to simulate the detailed response of a vehicle especially directly comparing to the experimental results. However the proposed model is more realistic especially when the road profile excitation is large and the tire loss contact with road surface. The numerical results show that the vibration characteristics of the car vibration system are mainly determined by the road profile excitation parameters. When the car moves on a minor road, it presents nonlinear characteristics. But as for the motorway, the road profile excitation amplitude is low, and the car vibration system is more likely to exhibit linearly characteristics. The period doubling bifurcation, well-know hardening type nonlinearity and the co-existing of stable periodic solutions are detected in the presented model.