中国物理B ›› 2008, Vol. 17 ›› Issue (8): 2753-2758.doi: 10.1088/1674-1056/17/8/001

• GENERAL •    下一篇

On the feasibility of variable separation method based on Hamiltonian system for plane magnetoelectroelastic solids

侯国林, 阿拉坦仓   

  1. Department of Mathematics, College of Science and Technology, Inner Mongolia University, Hohhot 010021, China
  • 收稿日期:2008-01-01 修回日期:2008-02-21 出版日期:2008-08-20 发布日期:2008-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10562002), the Natural Science Foundation of Inner Mongolia, China (Grant No 200508010103), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No 20070126002) and the Inner Mongolia University Doctoral Scientific Research Starting Foundation.

On the feasibility of variable separation method based on Hamiltonian system for plane magnetoelectroelastic solids

Hou Guo-Lin(侯国林)† and Alatancang(阿拉坦仓)   

  1. Department of Mathematics, College of Science and Technology, Inner Mongolia University, Hohhot 010021, China
  • Received:2008-01-01 Revised:2008-02-21 Online:2008-08-20 Published:2008-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10562002), the Natural Science Foundation of Inner Mongolia, China (Grant No 200508010103), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No 20070126002) and the Inner Mongolia University Doctoral Scientific Research Starting Foundation.

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摘要： The eigenvalue problem of an infinite-dimensional Hamiltonian operator appearing in the isotropic plane magnetoelectroelastic solids is studied. First, all the eigenvalues and their eigenfunctions in a rectangular domain are solved directly. Then the completeness of the eigenfunction system is proved, which offers a theoretic guarantee of the feasibility of variable separation method based on a Hamiltonian system for isotropic plane magnetoelectroelastic solids. Finally, the general solution for the equation in the rectangular domain is obtained by using the symplectic Fourier expansion method.

Abstract: The eigenvalue problem of an infinite-dimensional Hamiltonian operator appearing in the isotropic plane magnetoelectroelastic solids is studied. First, all the eigenvalues and their eigenfunctions in a rectangular domain are solved directly. Then the completeness of the eigenfunction system is proved, which offers a theoretic guarantee of the feasibility of variable separation method based on a Hamiltonian system for isotropic plane magnetoelectroelastic solids. Finally, the general solution for the equation in the rectangular domain is obtained by using the symplectic Fourier expansion method.

Key words: magnetoelectroelastic solid, variable separation method, completeness, general solution

中图分类号:  (Magnetomechanical effects, magnetostriction)

  • 75.80.+q
75.60.Ch (Domain walls and domain structure)