Symplectic Duality System on the Plane Magnetoelectroelastic Solids

YAO Wei-an; LI Xiao-chuan

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YAO Wei-an, LI Xiao-chuan. Symplectic Duality System on the Plane Magnetoelectroelastic Solids[J]. Applied Mathematics and Mechanics, 2006, 27(2): 177-185.

Citation:

YAO Wei-an, LI Xiao-chuan. Symplectic Duality System on the Plane Magnetoelectroelastic Solids[J]. Applied Mathematics and Mechanics, 2006, 27(2): 177-185.

Citation:

YAO Wei-an, LI Xiao-chuan. Symplectic Duality System on the Plane Magnetoelectroelastic Solids[J]. Applied Mathematics and Mechanics, 2006, 27(2): 177-185.

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Symplectic Duality System on the Plane Magnetoelectroelastic Solids

State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, P. R. China

Received Date: 2004-09-28
Rev Recd Date: 2005-10-17
Publish Date: 2006-02-15

Abstract

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 origin 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 eigen-solutions in Jordan form on eigenvalue zero can be given, and their specific physical significations were showed 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.
- magnetoelectroelastic solid,
- plane problem,
- symplectic geometry space,
- duality system,
- separation of variables

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References(8)

References

[1]	Benveniste Y.Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases[J].Phys Rev B,1995,51(22):16424—16427. doi: 10.1103/PhysRevB.51.16424
[2]	Huang J H,Kuo W S.The analysis of piezoelectric/piezomagnetic composites materials containing ellipsoidal inclusions[J].J Appl Phys,1997,81(3):1378—1386. doi: 10.1063/1.363874
[3]	Wang X,Shen Y P.The general solution of three-dimensional problems in magnetoelectroelastic media[J].International Journal of Engineering Science,2002,40(10):1069—1080. doi: 10.1016/S0020-7225(02)00006-X
[4]	刘金喜.各向异性电磁弹性介质的Green函数[J].石家庄铁道学院学报，2000,13(3):56—59.
[5]	姚伟岸.电磁弹性固体三维问题的广义变分原理[J].计算力学学报，2003,20(4):487—489.
[6]	姚伟岸，钟万勰.辛弹性力学[M].北京：高等教育出版社，2002.
[7]	钟万勰.应用力学对偶体系[M].北京：科学出版社，2002.
[8]	姚伟岸.电磁弹性固体反平面问题的辛求解体系及圣维南原理[J].大连理工大学学报，2004，44(5):630—633.