电磁场中载流薄板的弯曲行为分析

Analysis of Bending Performances of a Thin Current-carrying Plate in an Electromagnetic Field

在建立载流薄板的非线性磁弹性运动方程、电动力学方程和Lorentz力表达式的基础上,通过变量代换,将描述薄板的磁弹性状态方程整理成含有10个基本函数的标准Cauchy型。采用差分法及准线性化方法,将标准Cauchy型非线性偏微分方程组,变换成为能够用离散正交法求解的准线性微分方程组。通过算例,得到了电磁场与机械载荷联合作用下载流薄板的磁弹性应力与变形的数值解。变换电磁参量讨论了薄板的应力及变形的变化规律。结果表明,改变通电电流强度或者外加磁感应强度,可以改变载流薄板的应力与变形状态,达到控制薄板的受力与变形的目的。

Based on the nonlinear magnetoelastic kinetic equations,the electrodynamics equations,and the expressions of Lorentz force of thin current-carrying plate,normal Cauchy form nonlinear differential equations,which include ten basic functions in all,were obtained by variable replacement method.Using the difference and quasi-linearization methods,the nonlinear magnetoelastic equations were reduced to a sequence of quasilinear differential equations,which can be solved by discrete-orthogonalization method.The numerical solutions for magnetoelastic stresses and deformations in a thin current-carrying plate under the combined action of an electromagnetic field and mechanical load were obtained by considering a specific example.The results that the stresses and deformations in the thin plate change with variation of the electromagnetic parameters were discussed.The results show that the stresses and deformations in thin current-carrying plates can be controlled by changing the electric current density or the magnetic induction intensity.