非线性裂纹转子的分形分析

首先介绍了分形的基本概念，给出了机械振动信号主要应用的分析方法。然后研究了非线性裂纹转子的弯曲振动特性，给出了进入倍周期分叉后裂纹转子的时域特性和频域特性。最后对裂纹转子特性进行分形分析，发现并定义了裂纹转子在进入分叉以前轴心轨迹随裂纹角变化的分形特性，并发现裂纹转子在进入混沌前与进入混沌以后具有相似的分形特性；发现了裂纹转子带噪声信号具有两个分维数（二重分形）的复杂特性。

Fractal Analysis of Nonlinear Cracked Rotor

The basic concept of fractal and main methods applied to mechanical vibration signal analysis are presented. The bending vibration characteristic of a nonlinear cracked rotor is then analyzed. The time frequency characteristics of a cracked rotor after entering double cycle bifurcation are introduced. The characteristics of a cracked rotor are analyzed by the fractal method. The fractal property about shaft center orbit of a cracked rotor before entering bifurcation is found and defined when the shaft center orbit is changed along with the cracked angles. The study shows that the fractal property fo a cracked rotor after entering chaos is similar to that before entering chaos. There are two fractal dimensions (double fractal) in a noise contaminated signal of a cracked rotor.