| SYMPLECTIC DUALITY SYSTEM ON PLANE MAGNETOELECTROELASTIC SOLIDS |
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| 作者姓名： | 姚伟岸 李晓川 |
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| 作者单位： | State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of Technology Dalian 116023 Liaoning Province P. R. China，State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of Technology Dalian 116023 Liaoning Province P. R. China |
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| 摘 要： | By means of the generalized variable principle of magnetoelectroelastic solids, the plane magnetoelectroelastic solids problem was derived to Hamiltonian system. In symplectic geometry space, which consists of original variables, displacements, electric potential and magnetic potential, and their duality variables, lengthways stress, electric displacement and magnetic induction, the effective methods of separation of variables and symplectic eigenfunction expansion were applied to solve the problem. Then all the eigen-solutions and the eigen-solutions in Jordan form on eigenvalue zero can be given, and their specific physical significations were shown clearly. At last, the special solutions were presented with uniform loader, constant electric displacement and constant magnetic induction on two sides of the rectangle domain.
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| 关 键 词： | 电磁弹性固体 平面问题 偶对几何空间 对偶系统 变量分离 |
| 收稿时间： | 2004-09-28 |
| 修稿时间： | 2005-10-17 |
Symplectic duality system on plane magnetoelectroelastic solids |
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| Wei-an Yao,Xiao-chuan Li.SYMPLECTIC DUALITY SYSTEM ON PLANE MAGNETOELECTROELASTIC SOLIDS[J].Applied Mathematics and Mechanics(English Edition),2006,27(2):195-205. |
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| Authors: | Wei-an Yao Xiao-chuan Li |
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| Institution: | State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology, Dalian 116023, Liaoning Province, P. R. China |
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| Abstract: | By means of the generalized variable principle of magnetoelectroelastic solids, the plane magnetoelectroelastic solids problem was derived to Hamiltonian system. In symplectic geometry space, which consists of original variables, displacements, electric potential and magnetic potential, and their duality variables, lengthways stress, electric displacement and magnetic induction, the effective methods of separation of variables and symplectic eigenfunction expansion were applied to solve the problem. Then all the eigen-solutions and the eigen-solutions in Jordan form on eigenvalue zero can be given, and their specific physical significations were shown clearly. At last, the special solutions were presented with uniform loader, constant electric displacement and constant magnetic induction on two sides of the rectangle domain. |
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| Keywords: | magnetoelectroelastic solids plane problem symplectic geometry space duality system separation of variables |
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