四边简支载流矩形薄板的磁弹性动力屈曲分析  

MAGNETIC-ELASTISITY BUCKLING OF A RECTANGULAR THIN CURRENT PLATE SIMPLY SUPORTED AT EACH EDGE

作　　者：王知人[1] 王平[2] 白象忠[2] 

机构地区：[1]燕山大学理学院 [2]燕山大学建筑工程与力学学院

出　　处：《机械强度》2008年第3期422-427,共6页Journal of Mechanical Strength

基　　金：国家自然科学基金(50275128);河北省自然科学基金资助项目(A2006000190)~~

摘　　要：在载流薄板的磁弹性非线性运动方程、物理方程、几何方程、洛仑兹力表达式及电动力学方程的基础上,导出四边简支载流矩形薄板在电磁场与机械载荷共同作用下的磁弹性动力屈曲方程。应用Galerkin原理将该屈曲方程整理为Mathieu方程的标准形式,并利用Mathieu方程解的稳定区域与非稳定区域的分界,即方程系数的本征值关系,得出磁弹性问题屈曲临界状态的判别方程。通过具体算例,给出四边简支矩形板的磁弹性动力屈曲方程以及屈曲临界状态与相关参量之间的关系曲线,并对计算结果及其变化规律进行分析讨论。Based on the nonlinear magnetic-elasticity kinetic equations, physical equations, electrical kinetic equations and the expression of Lorentz force, the magnetic-elasticity kinetic buckling equation of a current plate applied mechanical load in a magnet field is given out. This equation is changed into the standard form of the Mathieu equation by using Galerkin method. The criterion equation of the magnetic-elasticity kinetic problem has been derived by the determination on the boundary line of steady and unsteady solution area of Mathieu equation, i.e. As an example, a rectangular plate simply supported at each edge is solved and its magnetic-elasticity kinetic buckling equation has been obtained here. The curves of the relations among the current density, the thickness of the plate and the current density, the magnetic strength when the plate is in the situation of critical buckling are shown. The conclusions may be the references for engineering application.

关 键 词：磁弹性 洛仑兹力 屈曲 MATHIEU方程 矩形薄板 

分 类 号：O441[理学—电磁学]