Symplectic Duality System on the Plane Magnetoelectroelastic Solids
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摘要: 从电磁弹性固体广义变分原理出发，将平面电磁弹性固体问题导入Hamilton体系．于是在由原变量——位移、电势和磁势以及它们的对偶变量——纵向应力、电位移和磁感应强度组成的辛几何空间，形成有效的分离变量及辛本征函数向量展开解法．求解出辛本征问题中特殊的零本征值所有本征解及其Jordan型本征解，并给出其具体的物理意义．最后求出在矩形域的两侧作用均布载荷、常电位移和常磁感应强度时的非齐次特解．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.
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[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. -
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