A type of viscoelastic material with variable viscoelastic parameters is introduced in the rear wheel compliance steering system to substitute the traditional rubber bushing. Based on the fractional order constitutive model of the viscoelastic material and the nonlinear Magic Formula tire model,the fractional order dynamic model of the vehicle with three degrees of freedom is built. According to the given parameters,the lateral dynamic behav-ior of the vehicle with rear wheel compliance steering is studied by means of MATLAB software. Research results show that,under the given parameters Hopf bifurcation of the rear wheel compliance steering angle occurs with ve-hicle speed increasing. When the vehicle speed is bigger than a threshold,vehicle shimmy happens and the period-ical vibration with two stable magnitudes appears in the time history curves of the rear wheel compliance steering an-gle and the vehicle yaw rate. And at the same time,two limit cycles appear in the phase diagram of the compliance steering angle. Parameters of the viscoelastic material have obvious effect on the nonlinear dynamic behavior of the vehicle with rear wheel compliance steering. a theoretical foundation for realization the semi-active control of the ve-hicle lateral dynamic behavior was established.%向后轮随动转向系统中引入一种黏弹性参数可变的黏弹性材料,以替代传统的橡胶衬套;基于黏弹性材料的分数阶本构模型,以及具有饱和特性的非线性魔术轮胎模型,建立了随动转向车辆的三自由度分数阶动力学模型;根据给定的车辆参数,利用MATLAB软件仿真研究了随动转向车辆的横向动力学行为.研究结果表明:在一定的参数条件下,随着车速的提高,后轮随动转向角发生了Hopf分岔现象;当车辆的行驶速度超过某个阈值时,随动转向车辆将发生明显的摆振,后轮随动转向角和车辆横摆角速度时间历程曲线均呈现出具有两个稳定幅值的周期振动,随动转向角相图上出现了两个极限环;后悬架中引入的黏弹性材料参数对随动转向车辆的非线性动力学行为具有明显的影响.该研究为后轮转向车辆横向动力学行为的半主动控制奠定了理论基础.
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