载流矩形薄板在电磁场中的屈曲分析

Magnetic-elastisity bucklig analysis of thin current-carrying plate

在载流薄板的磁弹性非线性运动方程、物理方程、洛仑兹力表达式及电动力学方程的基础上,导出了载流薄板磁弹性动力屈曲方程,并应用Galerkin原理把屈曲方程整理为Mathieu方程的标准形式,将载流矩形薄板在电磁场与机械荷载共同作用下的磁弹性屈曲问题归结为对Mathieu方程的求解问题。利用Mathieu方程系数λ和η的本征值关系,得出了载流薄板磁弹性动力屈曲临界状态的判别方程。并对不同边界条件、不同材料的矩形薄板进行了具体计算,给出了薄板的磁弹性动力失稳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了分析讨论。

Based on the magnetic-elasticity nonlinear kinetic equations, physical eq kinetic equations and the expression of Lorentz forces, the magnetic-elasticity uations, electrical kinetic buckling equation of a current-carrying plate applied mechanical load in a magnet field were derived. The equation was transformed into the standard Mathieu equation by using Galerkin method. Thus, the magnetic-elasticity kinetic problem was changed into a problem of solving the Mathieu equation. The criterion equation of the magnetic-elasticity kinetic problem was gotten by the eigenvalue relation of Mathieu equation＇s coefficient λ and η. The rectangular plates made of different materials were taken as calculating examples. The curves of the relations among the relative parameters are obtained when the plates are in the situation of critical buckling. The analysis and discussion of the calculating conclusion are given out.