马丢方程解的稳定性在磁弹性屈曲中的应用  

Applications of the stability of Mathieu equation’s solution in magnetic-elastisity buckling problem

作　　者：王平[1] 王知人[2] 白象忠[1] 

机构地区：[1]燕山大学建筑工程与力学学院,河北秦皇岛066004 [2]燕山大学理学院,河北秦皇岛066004

出　　处：《哈尔滨工业大学学报》2009年第11期222-224,共3页Journal of Harbin Institute of Technology

基　　金：国家自然科学基金资助项目(50875230)

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,应用Galerkin原理将屈曲方程整理为Mathieu方程的标准形式,并将薄板的动力屈曲问题归结为对Mathieu方程的求解.利用Mathieu方程解的稳定性,系数λ和η的本征值关系,导出了载流薄板磁弹性动力屈曲临界状态的判别方程,并给出了该方程当η为小激励时的稳定区域图.The magnetic-elasticity buckling problem of a current plate with applied mechanical load in a magnetic field is studied by using a special function,Mathieu function. Based on the non-linear magneto-elastic equations of motion,physical equations,geometric equations,expressions of Lorenz forces and electro-dynamic equations,the magneto-elastic dynamic buckling equation of a current plate under the action of mechanical load in a magnetic field is derived. Then the buckling equation is transmitted into a standard form of the Mathieu equation by using Galerkin method. Thus,the solving of buckling problem is changed to the solving of Mathieu equation. According to the solution’s stability of Mathieu equation and the eigenvalue relation of the coefficients λ and η in Mathieu equation,the criterion equation of the buckling problem is also presented here. And the map of the stability areas is shown when the coefficient η is small exciter.

关 键 词：磁弹性 稳定性 MATHIEU方程 屈曲 薄板 

分 类 号：O441[理学—电磁学]