非光滑碰撞振动系统动力学分析的Lyapunov指数判据  

THE CRITERION OF LYAPUNOV EXPONENTS FOR DYNAMIC ANALYSIS OF NON-SMOOTH VIBRO-IMPACT SYSTEMS

作　　者：金俐[1] 刘新华[1] 陆启韶[1] 

机构地区：[1]北京航空航天大学理学院,北京100083

出　　处：《工程力学》2006年第12期41-46,29,共7页Engineering Mechanics

基　　金：国家自然科学基金(10572011)资助项目

摘　　要：对n维非光滑(刚性约束和分段光滑)碰撞振动系统引进局部映射,利用Poincaré映射分析方法,建立了该类系统的Lyapunov指数谱与Floquet特征乘子之间的解析关系,提出了非光滑碰撞振动系统动力学分析的Lyapunov指数判据。以一类刚性约束的非线性碰撞振动系统为例,给出该系统的Lyapunov指数谱随参数大范围变化的规律,并将此规律与相应的Poincaré映射分岔图进行仔细对照,得到了一致的结论,验证了上述动力学分析的Lyapunov指数判据的正确性和有效性。The criterion of Lyapunov exponents is presented for dynamic analysis of non-smooth nonlinear dynamical systems by introducing n-dimensional non-smooth （rigid constraint and piecewise smooth） nonlinear dynamical systems, and by setting up some analytical relations between the spectrum of Lyapunov Exponents and Floquet characteristic multipliers of above systems by means of the Poincar~ map method. Finally, the spectrum of Lyapunov exponents in a large range of parameters is calculated for a given nonlinear dynamical system with rigid constraints. The stability, bifurcations and chaos of this given system are analyzed by applying the criterion of Lyapunov exponents. The results are compared with the bifurcation diagram of this given system obtained by the Poincar~ map method in the corresponding parameters range in order to validate correctness and validity of this criterion for dynamic analysis of non-smooth nonlinear dynamical systems.

关 键 词：非光滑碰撞振动系统 LYAPUNOV指数谱 POINCARÉ映射 Hoquct特征乘子 局部映射 

分 类 号：O322[理学—一般力学与力学基础]