非线性动力系统全局分析的变胞胞映射法与转子／轴承系统的全局稳定性

A Method of Alter Poincare Cell Mapping for Global Analysis of Nonlinear Dynamical System and the Stability of Rotor/Bearing System

在Ｐｏｉｎｃａｒé映射及胞映射理论的基础上，提出了一种非线性动力系统全局分析的新方法——变胞胞映射法（ＡＰＣＭ法），这种新方法改变了原胞映射法中胞在胞空间分布的不合理性及运算逻辑的不合理性，更适用于高维、大求解域非线性动力系统的求解。应用此方法，对具有非线性油膜力的Ｊｅｆｃｏｔ转子轴承系统进行了全局分析，绘制了系统分岔后的全局吸引域图。

Based upon the theories of the Poincare Mapping and the Cell to Cell Mapping, a new method called APCM for global analysis of multidimensional nonlinear dynamical system is presented in this paper. It is more justifiable than primary Cell to Cell Mapping for the distribution of cells in the Cell Space and the logicality of algorithm, and more suitable for the problem of the nonlinear dynamical system which has large analyzed domain. Using the method, the global stability of balanced `Jeffcot' rotor/bearing system which has nonlinear oil force is analyzed, and we obtained the pictures of their domain of the attraction, and explained some nonlinear phenomena usually happened in engineering.