非线性弯曲波摄动后的混沌行为  

The Chaos Behavior of Nonlinear Flexural Wave after Perturbation

作　　者：张善元[1] 刘志芳[1] 张涛[1] 

机构地区：[1]太原理工大学应用力学与生物医学工程研究所,太原030024

出　　处：《太原理工大学学报》2010年第4期323-327,共5页Journal of Taiyuan University of Technology

基　　金：国家自然科学基金资助项目(10772129)

摘　　要：在Bernoulli-Euler梁、Rayleigh修正梁和Timoshenko梁三种经典梁理论的基本方程中,分别引入有限挠度和轴向惯性,导出了相应的支配弯曲波传播的非线性偏微分方程组。采用行波解法,将每个方程组转化为对应的单个常微分方程。对派生方程的定性分析表明,在一定条件下这些方程在相平面上存在同宿轨道或异宿轨道,分别对应着孤立波解和冲击波解。将外加载荷和阻尼作为对系统的摄动,利用Melnikov函数给出了横截同(异)宿点出现的阈值条件,表明系统具有Smale马蹄意义下的混沌性质,从而揭示了孤立波与混沌两大类非线性现象之间的内在联系。On the basis of the equation of Bernoulli-Euler,Rayleigh and Timoshenko classic beam theories,taking finite-deflection and axial inertia into consideration,the nonlinear partial differential equations governing flexural wave propagation are derived.By employing the method of traveling wave solution,the nonlinear partial differential equations can be transformed into an ordinary differential equation.The qualitative analyses of derivation equations indicate that the three kinds of equations have heteroclinic orbit corresponding shock wave solution or homoclinic orbit corresponding solitary wave solution.The external load and damping are viewed as small perturbation into the system and the threshold condition of the existence of transverse homoclinic（heteroclinic） point is obtained by Melnikov＇s method.It is proved from this that the perturbed systems have chaotic property under Smale horseshoe transform meaning,which further reveal：the interrelationship between the two kinds of nonlinear phenomenon of solitary wave and chaos.

关 键 词：有限挠度梁 非线性波 混沌运动 MELNIKOV函数 

分 类 号：O347.4[理学—固体力学]