横向磁场中大挠度金属薄板的混沌振动  

The chaotic vibration of a metal plate with large deflection under a transverse magnetic field

作　　者：薛春霞[1] 张善元[2] 树学锋[2] 

机构地区：[1]中北大学理学院力学系,太原030051 [2]太原理工大学应用力学研究所,太原030024

出　　处：《物理学报》2010年第9期6599-6605,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10772129)资助的课题~~

摘　　要：利用Karman关于板的大挠度理论,考虑涡电流在板中引起的Lorentz力,导出了在横向磁场和横向载荷共同作用下薄板的非线性运动方程.借助Bubnov-Galerkin法将非线性偏微分方程转化为含三次非线性项的常微分方程.在定性分析的基础上,利用次谐轨道的Melnikov函数给出了发生Smale马蹄型混沌运动的阈值条件,进而数值计算了系统的分岔图、相应的相图、Poincaré映射和时程曲线,给出了混沌运动的数字特征.分析结果表明:磁感应强度和外载荷都会影响系统的振动特性.By using Karman’s plate theory of large deflection,the nonlinear equation of motion of a thin metal plate with the coaction of a transverse uniform magnetic field and a transverse load is established. These equations consider the magnetic Lorentz force induced by the eddy current. Based on the Bubnov-Galerkin method,the nonlinear partial differential equation is transformed into a third-order nonlinear ordinary differential equation. By using the sub-harmonic orbit Melnikov function method,the criterion of the Smale-horseshoe chaos is also acquired. Furthermore,the chaotic motion is numerically simulated with Matlab. The bifurcation diagram,the phase curve,the Poincaré map and the evolution curve are calculated. The digital characteristics of the chaotic motions are provided based on the analysis. The analysis results show that the magnetic induction intensity and the external load may affect the vibration of the system.

关 键 词：金属薄板 大挠度 横向磁场 混沌振动 

分 类 号：O322[理学—一般力学与力学基础]