一种确定非线性裂纹转子解的形式的新方法

将小波变换与Ｐｏｉｎｃａｒｅ映射相结合，即用Ｐｏｉｎｃａｒｅ映射确定周期解，用谐波小波变换区分拟周期响应和混沌运动，提出了一种分析非线性裂纹转子系统解的形式随参数变化的新方法．结果表明这种方法是非常有效的，它比以前所用的计算Ｌｉａｐｕｎｏｖ指数的方法节约了计算时间，并且较易实施．

A NEW METHOD OF IDENTIFYING THE TYPES OF MOTION OF A NONLINEAR CRACKED ROTOR 1)

A cracked rotor is a complicated nonlinear time-varying dynamical system and its types of motion can be periodic, quasiperiodic or chaotic when the parameters of system changes. For a given set of parameters of the system, Poincare section,power spectrum, wave form and Lyapunov exponent are usually utilized to see whether the response of the system is chaotic or not, but it is difficult to determine precisely the domains or attracting basins of different types of motions in parametric space or initial value space only from graphics study, and computing Lyapunov exponent is very time consuming. As wavelet transform can reveal local property in both time domain and frequency domain, a new method is introduced to identify the types of motions of the system, i.e., the periodic motions can be identified by Poincare map, and harmonic wavelet transform can distinguish quasiperiod and chaos since part or all of the harmonic components of a chaotic motion can't repeat periodically and can be noticed by the result of wavelet transform. Examples show that this method is more efficient than that of computing Liapunov exponent and can be easily applied to a nonlinear cracked rotor system.