用Poincar啨平面上的盒维数辨别非线性响应区域的方法研究  

IDENTIFICATION OF NONLINEAR REGIONS OF SYSTEM RESPONSES USING BOX DIMENSIONS OF POINCAR MAPS

作　　者：林富生[1,2] 张韬[1] 孟光[1] 

机构地区：[1]上海交通大学振动、冲击、噪声国家重点实验室,上海200030 [2]武汉科技学院机电工程系,武汉430073

出　　处：《机械强度》2004年第3期250-255,共6页Journal of Mechanical Strength

基　　金：国家"8 63"计划 (2 0 0 2AA41 2 4 1 0 )资助项目;"十五"国家科技攻关项目 (2 0 0 1BA2 0 4B0 5 KHKZ0 0 0 9)资助~~

摘　　要：提出一种计算Poincar啨映射平面的盒维数来区分系统响应中非线性特性区域的方法τ酶梅椒瓤膳斜餚oincar啨平面上的各种非线性响应形态 ,又可得到响应在Poincar啨平面上的分形维数氪撤中嗡惴?(如G P算法、改进G P算法、响应轨迹的盒维数算法等 )相比 ,本方法运算时间较短。文中给出一个计算实例 ,研究支承在挤压油膜阻尼器上的碰摩转子系统响应特征与Poincar啨平面上的盒维数之间的关系 。In the literature, most methods for calculation of the fractal dimension of a nonlinear system usually use the time series of the response. Herein a modified box-counting measure to calculate the box dimension of the Poincaré map of responses is proposed. Compared with the traditional G-P algorithm, the improved G-P algorithm and the box-counting approach, the computation time required for the proposed method was drastically reduced. The mode shapes of nonlinear vibratory systems are found to be associated with the box dimensions of Poincaré maps. The response is chaotic if the box dimension is less than 1.0, quasi-periodic if equal to 1.0, and periodic if equal to 2.0. The proposed method is demonstrated and validated by a numerical calculation of an impact-rub rotor system supported on squeezed film dampers. The bifurcation diagram of the rotor system was compared with the plot of the box dimension of Poincaré maps versus the corresponding control parameter. The great advantage of the proposed algorithm is the saving in the execution time, in addition to other advantages such as the possibility of identifying route to chaos.

关 键 词：盒维数 POINCARÉ映射 分形维数 非线性响应 混沌 

分 类 号：O322[理学—一般力学与力学基础] TP206.3[理学—力学]