Poincare型胞映射分析方法及其应用  

POINCARE-LIKE CELL MAPPING METHOD AND ITS APPLICATION

作　　者：刘恒[1] 虞烈[1] 谢友柏[1] 姚福生 

机构地区：[1]西安交通大学润滑理论与轴承研究所,西安710049 [2]机械工业部,北京100823

出　　处：《力学学报》1999年第1期91-99,共9页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金;西安交通大学博士基金

摘　　要：本文用Poincare型胞映射方法对平衡及不平．衡轴承转子非线性动力系统的全局特性进行了分析研究，同时求得了一定状态空间内系统存在的周期解及其在各不同Poincare截面上的吸引域，得到了一些新的现象和规律，并通过对平衡及不平衡轴承转子系统的全局特性异同的比较。A Poincare-like Cell Mapping method fit for both autonomous and periodic nonautonomous nonlinear dynamic systems is presented in this paper. Compared with the traditional Cell Mapping method, the new one has apparent advantages in practice due to introduction of Poincare section, and can be widely used in high dimension nonlinear dynamic systems. Using this new method, the global characteristic of balanced and unbalanced bearing rotor nonlinear dynamic systems are analyzed in this paper. The periodic solutions of these systems and their domains of attraction are given at the same time, so some new phenomenon and rules are got here. Comparing the global characteristic of balanced bearing rotor systems with that of unbalanced bearing rotor systems, some reference are given to establish the new stability rule for nonlinear balanced and unbalanced bearing rotor systems. At last, this paper also gives the theoretical explanation for great dispersion of logarithmic decrement of bearing rotor system.

关 键 词：非线性 胞映射 吸引域 轴承 转子 平衡 动力系统 

分 类 号：TH113.25[机械工程—机械设计及理论]