载流矩形薄板在交变磁场中的屈曲分析  

The Buckling of a Rectangular Thin Current-Carrying Plate in an Alternating Magnetic Field

作　　者：王平[1,2] 王知人[2,3] 白象忠[1] 王继利[3] 

机构地区：[1]燕山大学理学院,秦皇岛066004 [2]中国科学院力学研究所,非线性力学国家重点实验室(LNM),北京100080 [3]燕山大学建筑工程与力学学院,秦皇岛066004

出　　处：《力学季刊》2011年第4期539-546,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金资助项目(50875230);非线性力学国家重点实验室(LNM)开放基金资助项目(20101005)

摘　　要：以四边简支载流矩形薄板为例,在导出了载流薄板在电磁场与机械荷载共同作用下的磁弹性动力屈曲方程的基础上,应用伽辽金原理,将方程整理为马丢方程的标准形式。利用马丢方程解的稳定性,研究了薄板在交变磁场与机械荷载共同作用下的磁弹性屈曲问题。通过具体算例,给出了该矩形薄板在交变磁场中,动力屈曲临界状态与相关参量之间的关系曲线及变化规律,并与均匀磁场作用下的情形相比较。研究结果表明:变化电磁场的性质和大小,改变通电电流参数,均可改变电磁力的状态,从而可达到控制载流薄板屈曲的目的。A rectangular thin current-carrying plate is simply supported at each edge.Based on deriving the magnetic-elasticity dynamical buckling equation of the plate applied mechanical load in a magnet field,the equation was changed into the standard form of the Mathieu equation by using the Galerkin＇s method.The magnetic-elasticity buckling problem of the plate applied mechanical load in an alternating magnet field was studied by using the solution＇s stability of the Mathieu equation.As an example,a current carrying rectangular plate is simply supported at each edge in an alternating magnet field,and the curves of the relations among the relative parameters when the plate is in the situation of critical buckling are shown and compared with in an uniform magnetic field here.The conclusions show that the electro-magnetic forces may be controlled by changing the parameters of the current and the magnetic field to get the aim for controlling the buckling of the current carrying plate.

关 键 词：交变磁场 薄板 屈曲 马丢方程 

分 类 号：O441[理学—电磁学] O482.6[理学—物理]