摘要
本文利用马丢方程,研究载流薄板在电磁场与机械荷载共同作用下的磁弹性动力失稳问题。在导出载电流薄板在电磁场与机械荷载共同作用下的磁弹性动力稳定性方程的基础上,应用Galerkin原理将稳定性方程整理为马丢方程的标准形式,将薄板的动力稳定性问题归结为马丢方程的求解。并利用马丢方程的稳定解区域与非稳定解区域的分界,即方程系数λ和η的本征值关系,以三边简支一边自由载流矩形薄板为例,得出了载流薄板磁弹性动力失稳临界状态的判别方程。
The magnetic-elasticity kinetic stability problem of a current carrying plate under the action of mechanical load in a magnet field is studied by using the Mathieu equation. Based on deriving the magnetic-elasticity kinetic steady equation, the equation is changed into the standard form of the Mathien equation by using the Galerkin method. Solving the Mathieu equation can then get the solution of the stability problem. Through discussing the boundary lines of steady and unsteady solution areas of the Mathien equation, that is, discussing the eigenvalue relations between tile coefficients λ and η in the Mathieu equation, the magnetic-elasticity criterion equation of a plate simply supported at three edges has been gotten as an example.
出处
《工程数学学报》
CSCD
北大核心
2006年第1期133-138,共6页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(50275128)
关键词
磁弹性
稳定性
马丢方程
失稳
薄板
magnetic-elasticity
stability
the Mathieu equation
buckling
thin plate
