In this paper, the dynamic behavior of a quarter-car with two degree-of-freedom which consists of sprung mass and unsprung mass is examined. Nonlinearity occurred due to nonlinear hysteretic suspension damper and spring. Vehicle tire is modeled as a nonlinear hardening spring. The disturbance of road assumed to be sinusoid. Frequency response diagram of the model has been obtained. Results show that the dynamic response of the vehicle can be chaotic. Influence of road roughness amplitude on vehicle vibration is investigated and critical amplitude of the road surface profile is found, above which the system can vibrate chaotically. The comparison between the results obtained from the proposed model and those from the single degree-of-freedom quarter-car model shows that the unsprung mass has great influence on the dynamical behavior of the system, which cannot be ignored.

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