用谐波小波变换法研究船舶横摇的非线性动力特性

本文探索了一种用小波分析的方法来研究船舶非线性横摇系统的运动.对于非线性非自治系统的响应主要有周期、准周期和混沌几种状态.而在系统参数变化时,又由周期分叉形成了准周期和混沌.因此,需要对周期解做更多的研究.当系统响应是周期的,通过小波变换,可以得到一些不同频率的谐波,这些谐波与谐波平衡法得到的解非常相似,因此也就可以作为系统的近似解.如果系统响应是混沌的,通过小波变换,始终都得不到周期的信号,这一点明显区别于周期运动.也就是说通过小波变换这种方法,可以明显地区别出混沌和周期.

Nonlinear Dynamical Character of Ship Rolling Investigated by Harmonic Wavelet Transform

A method of using harmonic wavelet transform to analyze the nonlinear system of ship rolling is explored.The fundamental response of a nonlinear nonautonomous system is periodic,quasi-periodic and chaotic motion.And quasi-periodic and chaotic motion can bifurcate from periodic motion when parameters of the system are changed.Therefore,it is required to investigate the periodic solution further.When the response is periodic,by the harmonic wavelet transform,some harmonics with different frequency will be obtained,which are similar to the results by harmonic balance method.When the response is chaotic,by the wavelet transform,there is no any periodic signal,which is the fundamental difference from periodic motion.It is shown that chaotic motion can be easy distinguished from periodic one by this method.