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受扰细杆的Melnikov分析
引用本文:赵广慧,张年梅,杨桂通.受扰细杆的Melnikov分析[J].力学学报,2005,37(4):511-515.
作者姓名:赵广慧  张年梅  杨桂通
作者单位:太原理工大学应用力学研究所,030024
基金项目:国家自然科学基金(10172063),山西省青年科学基金(20051004)和太原理工大学青年基金(12901116)资助项目.
摘    要:研究了计入Peierls-Nabarro (P-N)力和固体黏性效应的一维金属杆在简谐外力扰动下的动力响应,其位移波的运动规律是Sine-Gordon (SG) 型方程. 采用集结坐标 (collective coordinate)将方程的解设为未扰系统呼吸子解的形式,研究扰动作用下,组成呼吸子的扭结-反扭结波的中心的分离. 通过用集结坐标表示系统的哈密顿量,从而将SG型方程转化为常微分方程组. 分析了未扰系统的异宿轨道,并将之用于Melnikov方法对系统进行分析,给出横截异宿点出现的必要条件,从而预测混沌运动的发生.

关 键 词:集结坐标  Sine-Gordon方程  Melnikov方法  异宿轨道  混沌  
文章编号:0459-1879(2005)04-0511-05
收稿时间:2004-04-25
修稿时间:2005-03-03

Melnikov analysis of the perturbed thin bar
Zhao Guanghui,Zhang Nianmei,Yang Guitong.Melnikov analysis of the perturbed thin bar[J].chinese journal of theoretical and applied mechanics,2005,37(4):511-515.
Authors:Zhao Guanghui  Zhang Nianmei  Yang Guitong
Abstract:The dynamical response of one-dimensional metal bar considering Peierls-Nabarro force and viscous effect of solid has been researched. Movement of displacement wave in the bar follows SG type equation. According to "Collective coordinate approach", solution of the SG type equation is assumed as breather-type solution of undisturbed system. Separation between the center of mass of the kink and the anti-kink that make up the breather is researched under perturbation. The partial differential equation is reduced to the ordinary differential equation through describing the Hamiltonian of the system with collective coordinate. The hetero-clinic orbit of unperturbed system is analyzed through potential function and this is used in Melnikov method. Necessary condition for appearance of the cross-sectional heteroclinic point is given to forecast happening of chaotic.
Keywords:collective coordinate  Sine-Gordon equation  Melnikov method  heteroclinic orbit  chaos
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