双频激励下含分数阶非线性汽车悬架系统的混沌研究  

Chaos of vehicle suspension system with fractional order nonlinearity under dual frequency excitation

作　　者：常宇健 孙亚婷[1] 陈恩利 李韶华[2] 邢武策[2] CHANG Yu-jian;SUN Ya-ting;CHEN En-li;LI Shao-hua;XING Wu-ce(School of Electrical and Electronic Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)

机构地区：[1]石家庄铁道大学电气与电子工程学院,河北石家庄050043 [2]石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室,河北石家庄050043

出　　处：《振动工程学报》2021年第6期1198-1206,共9页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(12072205)。

摘　　要：研究了含分数阶非线性特性的1/4汽车悬架模型在双频激励下的混沌运动。运用Melnikov方法,推导出系统发生异宿混沌运动的解析必要条件,得到系统混沌边界曲面阈值,讨论了悬架系统各参数对混沌边界曲面的影响。运用时间历程图、频谱图、相图、庞加莱截面图及最大李雅普诺夫指数进行数值验证。研究表明,在双频激励下悬架系统存在混沌运动,且含分数阶非线性悬架系统中阻尼系数、刚度系数等各参数对混沌边界曲面阈值都有一定影响,其中分数阶项阶数和系数及线性阻尼系数对其影响较大。The chaotic motion of 1/4 vehicle suspension model with fractional nonlinear characteristic under dual frequency excitation is studied.Using the Melnikov method,the analytical necessary conditions for heteroclinic chaotic motion of the system are derived,and the threshold of the chaotic boundary surface of the system is obtained.The influence of various parameters of the suspension system on the chaotic boundary surface is discussed.Time history diagram,spectrum diagram,phase diagram,Poincarécross section diagram and maximum Lyapunov index are used for numerical verification.The results show that there is chaotic motion in the suspension system under dual frequency excitation,and the damping coefficient,stiffness coefficient and other parameters have certain influence on the threshold value of the chaotic boundary surface in the suspension system with fractional order,in which the fractional order term and coefficient and linear damping coefficient have great influence.

关 键 词：非线性振动 汽车悬架 混沌运动 双频激励 分数阶 

分 类 号：O322[理学—一般力学与力学基础] U463.33[理学—力学]