【作者】 胡波；

【导师】 白象忠；

【作者基本信息】 燕山大学 ， 工程力学， 2004， 硕士

【摘要】 电磁弹性系统中的杆、薄板、薄壳等，当没有机械约束时，系统至少存在一个不稳定的运动模态，而存在约束时，当电流或磁场达到某一临界值后，系统将发生屈曲。因此，杆、薄板、薄壳等的磁弹性稳定问题分析是一个重要的理论和应用问题。以前，对磁弹性稳定性理论的研究主要集中以下两方面：一、软铁磁性薄板屈曲理论模型的建立及修正；二、以Tokamak核聚变反应堆环向磁场载流线圈为代表的对载流线圈及载流杆件的稳定性研究。而对工程中屡见不鲜的在强磁场作用下的载流薄板、薄壳等结构元件的稳定性研究则尚未见诸文献。本文将载流构件磁弹性稳定问题由线圈、杆件拓展到载流薄板，并引入特殊函数判别磁弹性稳定问题的失稳临界状态，得到了相关参量的数值关系。首先通过理论推导给出了载流薄板的磁弹性动力学方程，几何与物理方程，洛仑兹力的表达式，电动力学方程。并在此基础上，得出了载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。然后，应用Galerkin原理将稳定性方程整理为特殊函数马丢方程的标准形式，并利用马丢方程的稳定解区域与非稳定解区域的分界，即系数和的本征值关系得出了磁弹性最低失稳临界状态的判别方程。最后，通过具体算例，得出了四边简支、三边简支一边自由、对边简支对边固定、四边固定四种边界条件下矩形薄板的磁弹性动力稳定方程以及失稳临界状态时相关参量之间的关系曲线，并对其变化规律进行了分析讨论。得出了外加磁感应强度的变化对载流薄板的失稳临界电流密度影响极大，减小外加磁感应强度可以有效地提高失稳临界电流密度等结论。更多还原

【Abstract】 Pole , thin plate , thin shell in the electromagnetic elastic system ,etc. when there is no machinery to restrain, the system has an unstable movement mode at least, and while exists restrain, after up to a certain critical value in electric current or the magnetic fielding, buckling must take place in the system. So, the magnetoelastic stability analysis of the pole , thin plate , thin shell is an important theory and question of using.In the past, two following respects that the study on magnetoelastic stability theory was main and centralized : First , setting-up and revision of the soft ferromagnetism plates buckling theory model; Second, represented by the Tokamak Thermonuclear current-carrying Rector Coil, the stability of current-carrying coils and poles under magnetic field has been studied. However, it has not been seen in all documents yet that the study of stability of thin current-carrying plates and shells, etc. structure under strong magnetic field which is common occurrence to project. This text expanded the magnetoelastic stability issue of current-carrying component from coil , pole piece to thin current-carrying plates, and used special function to differentiate the critical state of losing magnetoelastic steady, the number value of getting the relevant parameter is solved .The text derives and provides the magnetoelastic movement equation of thin current-carrying plates, the geometry equations and the physics equations, the expression formula of Lorent’s force, electro dynamics equation through the theory at first. On this basis, draw magnetoelastic movement stability equation of thin current-carrying plates under the effect of electric magnetic field and machinery load. Then, use Galerkin principle to put the stability equation in order for the special function the Mathieu standard form, and utilize the boundary of the Mathieu solves’ steady area and unsteady area , namely special relationships of and,draw the discrimination equation of losing the magnetoelastic steady critical state. Finally, through regarding as the example concretely, relation curve between the relevant parameters while losing the magnetoelastic steady critical state were drawn in four kinds of different border conditions plate, and analyses about its change law. Have drawn the <WP=6>following conclusion: the intensity of magnetic field outside has a great influence to the density of the electric current of lose steady of thin current-carrying plates, and reduce the intensity of magnetic field can effectively increase the density of the electric current of lose steady,etc.更多还原