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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