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 industion, 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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References
Benveniste Y. Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases[J]. Phys Rev B, 1995, 51(22): 16424–16427.
Huang J H, Kuo W S. The analysis of piezoelectric/piezomagnetic composites materials containing ellipsodial inclusions[J]. J Appl Phys, 1997, 81(3): 1378–1386.
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.
Liu Jinxi. Green’s functions for anisotropic electron agnetic elastic media[J]. Journal of Shijiazhuang Rail Way Institute, 2000, 13(3): 56–59(in Chinese).
Yao Wei’an. The generalized variational principles of three-dimensional problems in magantoelectroelastic solids[J]. Chinese Journal of Computational Mechanics, 2003, 20(4): 487–489(in Chinese).
Yao Wei’an, Zhong Wanxie. Symplectic Elasticity[M]. Higher Education Press, Beijing, 2002(in Chinese).
Zhong Wanxie. Duality System of Application Mechanics[M]. Science Press, Beijing, 2002(in Chinese).
Yao Wei’an. Symplectic solution system and the Saint-Venant principle on the anti-plane problem of magnetoelectroelastic solids[J]. Journal of Dalian University of Technology, 2004, 44(5): 630–633(in Chinese).
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Project supported by the National Natural Science Foundation of China (No. 10172021)
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Yao, Wa., Li, Xc. Symplectic duality system on plane magnetoelectroelastic solids. Appl Math Mech 27, 195–205 (2006). https://doi.org/10.1007/s10483-006-0207-z
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DOI: https://doi.org/10.1007/s10483-006-0207-z