基于矢量椭球面波函数展开的椭球体电磁感应研究  

Research on electromagnetic induction based on vector spheroidal wavefunctions expansion for spheroid

作　　者：赵海军[1] 余梅 贺春林[1] 崔梦天[2] 

机构地区：[1]西华师范大学计算机学院,四川南充637009 [2]西南民族大学计算机科学与技术学院,四川成都610041

出　　处：《吉林师范大学学报（自然科学版）》2018年第1期78-84,共7页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(61379019);西华师范大学基本科研业务费专项基金项目(14C002);南充市科技支撑项目(15A0068)

摘　　要：由于椭球体模型存在于许多实际工程和科学研究中,对其电磁感应特性的研究一直以来都受到人们的广泛关注.基于此,本文对具有导电和渗透性能的椭球体的电磁感应特性进行了研究.具体做法是首先得到椭球体内部满足矢量波动方程的磁场和可以表示为拉普拉斯解的梯度的外部磁场,然后在椭球面坐标系中采用分离变量法,对磁场按照矢量椭球面波函数进行展开,得到任意初始激励下的磁解;最后对轴向和横向激励情况下的归一化感应磁偶极矩在宽频段范围进行了数值仿真,得到了依赖于感应数的电磁感应特性.Due to spheroidal models existing in many paractical engineerings and scientific researchs,the electromagnetic induction characteristic research for them draw peoples close attention to all the time. In view of this,the electromagnetic induction characteristic research for conducting and permeable spheroids is studied. The concrete implement is that the magnetic field inside the spheroid satisfying the vector wave equation and the magnetic field outside can expressed as the gradient of the Laplace solution is first obtained,and then the magnetic field solution is derived under arbitrary primary field excitation using the separation of variables method in spheroidal coordinates system by expanding the magnetic field in terms of vector spheroidal wavefunctions. The electromagnetic induction characteristic depended on the induction number is shown by the simulation of the normalized induced magnetic dipole moment under the axial excitation and transverse excitation in the broadband limit finally.

关 键 词：椭球面坐标系 矢量波函数 电磁感应 激励 磁偶极矩 

分 类 号：O441.3[理学—电磁学]