具有间隙和带负阻尼的机械系统自激振动理论及应用

THEORY AND APPLICATIONS OF SELF-EXCITED VIBRATION WITH CLEARANCE AND NEGATIVE DAMPING IN MECHANICAL SYSTEMS

自激振动理论问题归结为极限环论的研究。几乎所有的学者只针对极限环内含奇点的情况，讨论了极限环的存在性、唯一性、稳定性以及如何产生与消失。从具有间隙的机械系统中提出了一个新的力学模型，它不满足通常的极限环存在性、唯一性和稳定性的条件，称为广义Ｌｉｅｎａｒｄ方程。给出了其极限环存在性、唯一性以及稳定性的证明。数值求解给出了奇线段对极限环影响的一些有兴趣的结果。所得到的结论不仅对轧钢机设计与生产有很大的实际意义，还可以推广到转子轴承系统、擒纵机构等的研究。

Theory of self-excited vibration belongs to the study on the theory of limit cycles.Almost all of scholars only studied the possible appearance or disappearance of a limit cycle surrounding a singular Point.A new mathematical model with clearance is Presented.It is not satisfied general condition for existence of a stable limit cycle. Because there is a singular segmental line,this equation is called generalized Lienard equation.Authors give two theorems about the existence and uniqueness of stable limit cycle of this equation,then the numerical computation can be used to solve generalized Lienard equation,some new conclusins are obtained which are useful for self-excited vibration of mechanical engineering.