汽车转向轮摆振的稳定性及分岔行为分析

研究了减小和消除汽车转向轮摆振的方法.以三自由度前桥转向轮模型为研究对象,利用常微分方程稳定性理论和数值分析得出系统除零平衡点外其他平衡点都不会发生Hopf分岔,而且发现改变某些参数可以完全消除摆振,改变某些参数对系统摆振没有明显影响,改变某些参数还可以引起二次摆振.针对零平衡点,利用中心流形理论和规范形理论对系统进行化简并对约化方程进行分析,得到其分岔特性.进一步地,运用奇异性理论发现该系统的分岔特性在小扰动下具有很好的保持性.

STUDY ON STABILITY AND BIFURCATION BEHAVIOR OF A CAR TURNING WHEEL SHIMMY

The manner that reduces and eliminates a car turning wheel shimmy is studied.Stability of all equilibrium positions of the front bridge and turning wheel model with three degrees of freedom is studied by the stability theory of ordinary differential equations and numerical analysis method.A Hopf bifurcation does not occar for all equilibriwn positions except the zero position.And changing of some parameters will result in disappearing of the car turning wheel shimmy,and some do not influence the shimmy and some will result in appearing of the second shimmy.At the zero position,the centre manifold theory and the normal form method are introduced in order to obtain explicit expressions of the averaged equation,and the complicated dynamic behavior is discovered.Furthermore,using the singularity theory,it is discovered that the bifurcation characteristics possesses good persistence under small perturbations.