A NEW METHOD OF IDENTIFYING THE TYPES OF MOTION OF A NONLINEAR CRACKED ROTOR 1)
一种确定非线性裂纹转子解的形式的新方法

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.