非线性车辆悬架系统的滞后分岔及多稳态控制  

Hysteresis Bifurcation and Control Multistability of Nonlinear Vehicle Suspension System

作　　者：贺尔星 赵文浩 刘润 李高磊 乐源[1] He Erxing;Zhao Wenhao;Liu Run;Li Gaolei;Yue Yuan(SApplied Mechanics and Structure Safety Key Laboratory of Sichuan Province,School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu 610031)

机构地区：[1]西南交通大学力学与航空航天学院应用力学与结构安全四川省重点实验室,成都610031

出　　处：《动力学与控制学报》2023年第3期30-36,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11672249,12072291,11732014)。

摘　　要：考虑一类单自由度1/4非线性车辆悬架系统,根据Floquet理论得到周期运动的Floquet乘子用于判定其稳定性;并得到Lyapunov指数用于刻画混沌运动的性质.揭示了系统中一种新的滞后分岔:滞后环由一条稳定的周期轨道、一条不稳定周期轨道和一条周期轨道的倍化序列构成.其中周期轨道的倍化序列在滞后环的边界已经形成混沌轨道;因此随参数改变在该滞后环边界将产生一条稳定周期轨道与一条混沌轨道之间的跳跃现象.并且,若周期倍化序列形成的混沌轨道在滞后环边界处与不稳定周期轨道接触,混沌轨道将产生边界激变而突然消失,并跳跃至另一条稳定的周期轨道.根据线性增益控制法,实现了滞后环内部的多稳态控制,包括从大振幅周期3轨道控制到小振幅周期1轨道,以及周期1轨道控制到混沌轨道.本文研究结果可为车辆悬架的动力学设计提供理论参考.A single-degree-of-freedom quarter suspension system is considered.According to the theory of Floquet,we can get the Floquet multiplier which is employed to determine the stabled of period trajectory and the Lyapunov exponent which is employed to determine the nature of chaos motion.We reveal a new hysteresis bifurcation:hysteresis loop is composed of a stable period trajectory and an unstable period trajectory,the stable period trajectory which has a complete priod-dobubling sequence.The priod-dobubling sequence has appeared a chaos trajectory on the boundary of the hysteresis loop,so there will occur jumping phenomena between the stable period trajectory and the chaos trajectory on the boundary of the hysteresis loop as the change of parameters.In addition,if the chaos trajectory formed by priod-dobubling sequence meets with unstable trajectory on the boundary of the hysteresis loop,the chaos trajectory will occur boundary crisis and disappeared suddenly,then jumps to the other stable trajectory.According to the method of linear augmentation control,the multistability is controlled which insides of hysteresis loop,including the high amplitude 3-period trajectory has controlled to low amplitude 1-period trajectory and 1-period motion has controlled to chaos motion.The results of the research can provide theoretical reference for the dynamics design of vehicle suspension.

关 键 词：非线性车辆悬架 滞后分岔 周期倍化序列 边界激变 多稳态控制 

分 类 号：O313[理学—一般力学与力学基础]