含刚性及弹性约束的振动系统的动力学特性  

Dynamic Characteristics of a Vibration System with Rigid and Elastic Constraints

作　　者：王世俊[1] 马琳[1] WANG Shi-jun;MA Lin(School of Mechatronic Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学机电工程学院,兰州730070

出　　处：《兰州交通大学学报》2020年第5期76-81,104,共7页Journal of Lanzhou Jiaotong University

摘　　要：机械系统中一般同时存在刚性约束和弹性约束,不同约束形式会对振动系统动力学行为产生不同的影响.因此建立了具有刚性及弹性复合约束的两自由度受迫振动系统的动力学模型,分析了复杂受力情况下粘滞运动的发生条件.采用四阶Runge-Kutta数值积分法,结合分岔图、相图、时间历程图,研究了系统在低频条件下相邻基本周期冲击振动的转迁规律,讨论了弹性约束刚度比μ0对于系统冲击振动特性的影响.结果表明:Real Grazing分岔将导致基本周期运动p/1冲击次数p增加一次而进入稳定的(p+1)/1运动,Bare Grazing分岔将使系统进入含有亚谐运动、概周期运动、混沌运动的转迁域.复合约束条件下Bare Grazing分岔还可能会激发半环状周期窗口.弹性约束刚度比μ0越小,则系统冲击振动的模式类型越简单,μ0越大则将引入更多的亚谐运动、概周期运动和混沌运动.Mechanical systems generally have both rigid and elastic constraints,and different forms of constraints will have different effects on the dynamic behavior of the vibration system.Therefore,a dynamic model of a two-degree-of-freedom forced vibration system with rigid and elastic compound constraints is established,and the occurrence conditions of sticking motion under complex force conditions are analyzed.By using the four order Runge-Kutta numerical integration method,combining with bifurcation diagrams,phase diagrams,and time series diagrams,the transition law of the fundamental impact motions of the system under low frequency conditions is studied.The influence of elastic constrained stiffness ratio μ 0 on the system's shock and vibration characteristics is discussed.It is found that the real grazing bifurcation will increase the impacts number of fundamental periodic motion p /1 by one time and lead to a stable ( p +1)/1 motion,while the bare grazing bifurcation will lead the system into a transition domain containing sub harmonic motions, quasi-periodic motions,and chaotic motions.Bare Grazing bifurcation under compound constraints may excite a semi-cyclic periodic window.The smaller the elastic constrained stiffness ratio μ 0 is,the simpler the form of impact motions is;The larger the μ 0 is,the more sub-harmonic motions,quasi periodic motions and chaotic motions will be introduced.

关 键 词：非线性动力学 低频特性 分岔 碰撞振动 复合约束 

分 类 号：O322[理学—一般力学与力学基础] TH113.1[理学—力学]