载流环形板的热磁弹性分析  

Analysis of Thermal-Magneto-Elasticity for the Current-Carrying Annular Plate

作　　者：田振国[1] 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

出　　处：《中北大学学报（自然科学版）》2009年第1期8-15,共8页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(50275128);河北省自然科学基金资助项目(A2006000190)

摘　　要：对置于磁场中的载流环形板的热磁弹性问题进行了理论分析,讨论了载流板的温度、应力、位移与外加电磁场、温度场以及机械载荷的关系.首先根据电动力学方程和广义欧姆定律得到了载流薄板的电流密度的分布,考虑到焦耳热效应及热平衡方程,得到了由于焦耳热效应产生的置于磁场中的载流环形板的温度场;同时引入了热传导方程,得到了外加温度场引起的环形板内部的温度分布,并认为两种温度场相互独立且满足叠加原理,从而得到了载流环形板的温度分布.其次在建立载流板壳的电磁场、温度场、机械场耦合非线性运动方程,物理方程、几何方程及电动力学方程的基础上,得到了板壳热磁弹性问题的基本方程.最后应用准线性迭代方法,得到了关于热磁弹性问题的线性迭代方程组,整理成含有8个基本未知函数的标准柯西型,即变换成能用离散正交法编程求解的准线性微分方程组,应用自编程序,得到该问题的数值解.变换电磁参量,讨论了载流环形薄板应力、温度及变形随外加电磁参量的变化规律;根据圆环形板的挠度与参量之间的变化规律,并通过实例证实了可以通过改变电、磁、力场的参数来实现对板壳的应力、应变状态的控制.The problem of thermal-magneto-elasticity is analyzed theoretically for the current carrying annular plate in magnetic field. It is discussed that the relationship among the electromagnetic field, thermal field, mechanic load and temperature, stress, displacement in the thin current plate. First, the distribution of the current density is obtained based on the electrodynamics equations and thermal Ohm law. Considering the Joule＇s heat effect and thermal equilibrium equation, the temperature field produced by the Joule＇s heat effect is got in the current annular thin plate which is placed in the magnetic field. At the same time, the temperature field produced by the external thermal load is got by the heat transfer equation in the annular plate. Assuming two kinds of temperature fields are separate and satisfy the principle of superposition, the heat distribution of the current carrying annular plate can be got. Second, based on the nonlinear kinetic equation of coupling electromagnetic equation, geometrical equation and electrodynamics equation of the current-carrying plate, the basic equations of thermal-magneto-elastic problem are obtained. At last, applying the quasi-linearization iteration method, a sequence of linear iteration ordinary differential equations are obtained and transformed into the normal Cau the discrete ort deformation of parameters. Ac proved that the parameters.

关 键 词：载流薄板 耦合场 焦耳热 电磁力 热磁弹性 

分 类 号：O343[理学—固体力学] O482.5[理学—力学]