中文摘要：

针对三边简支、一边自由的载流矩形薄板,利用马丢方程解的稳定性,研究在交变磁场与机械载荷共同作用下的磁弹性稳定性问题。在导出载流薄板在电磁场与机械载荷共同作用下的磁弹性动力稳定方程的基础上,应用伽辽金原理将方程整理为马丢方程的标准形式。利用马丢方程系数的本征值关系,得出载流薄板磁弹性动力失稳临界状态的判别方程。通过具体算例,给出该矩形薄板在交变磁场中,动力失稳临界状态与相关参量之间的关系曲线及变化规律,并与均匀磁场中情形相比较。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,从而达到控制载流薄板稳定性的目的。

英文摘要：

For a current carrying rectangular plate which is simply supported at three edges,the magnetic-elasticity steady problem of the plate applied mechanical load in an alternating magnetic field is studied by using the solution＇s stability of the Mathieu equation.Based on deriving the magnetic-elasticity dynamic stability equation of the plate applied mechanical load in a magnetic field,the equation is changed into the standard form of the Mathieu equation by using the Galerkin method.The criterion equation of the magnetic-elasticity steady problem of the plate has been gotten here through analyzed the eigen value relations between the coefficients in the Mathieu equation.As an example,for a current carrying rectangular plate simply supported at three edges in an alternating magnetic field,the curves of the relations among the relative parameters when the plate is in the situation of critical steady are shown in here.The conclusions show that the electro-magnetic forces may be controlled by changing the parameters of the current and the magnetic field so that to get the aim for controlling the stability of the current carrying plate.