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CLC number: O343.2; O343.8; TB39

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Received: 2005-02-18

Revision Accepted: 2005-06-10

Crosschecked: 0000-00-00

Cited: 6

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Citations:  Bibtex RefMan EndNote GB/T7714

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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.9 P.922~927

10.1631/jzus.2005.A0922


A symplectic eigensolution method in transversely isotropic piezoelectric cylindrical media


Author(s):  XU Xin-sheng, GU Qian, LEUNG Andrew Y. T., ZHENG Jian-jun

Affiliation(s):  State Key Laboratory of Structure Analysis of Industrial Equipment and Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China; more

Corresponding email(s):   xsxu@dlut.edu.cn

Key Words:  Symplectic method, Hamiltonian system, Transverse isotropic, Piezoelectric media, Eigensolution


XU Xin-sheng, GU Qian, LEUNG Andrew Y. T., ZHENG Jian-jun. A symplectic eigensolution method in transversely isotropic piezoelectric cylindrical media[J]. Journal of Zhejiang University Science A, 2005, 6(9): 922~927.

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author="XU Xin-sheng, GU Qian, LEUNG Andrew Y. T., ZHENG Jian-jun",
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2005.A0922


Abstract: 
This paper reports establishment of a symplectic system and introduces a 3D sub-symplectic structure for transversely isotropic piezoelectric media. A complete space of eigensolutions is obtained directly. Thus all solutions of the problem are reduced to finding eigenvalues and eigensolutions, which include zero-eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian matrix and non-zero-eigenvalue solutions. The classical solutions are described by zero-eigensolutions and non-zero-eigensolutions show localized solutions. Numerical results show some rules of non-zero-eigenvalue and their eigensolutions.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[3] Ding, H.J., Chen, B., Liang, J., 1996. General solutions for coupled equations for piezoelectric media. Int. J. Struct., 33:2283-2298.

[4] Ding, H.J., Guo, F.L., Hou, P.F., Zou, D.Q., 2000. On the equilibrium of piezoelectric bodies of revolution. Int. J. Solids Structures, 37:1293-1326.

[5] Ding, H.J., Xu, R.Q., Chen, W.Q., 2002. Free vibration of transversely isotropic piezoelectric circular cylindrical panels. Int. J. Mech. Sci., 44:191-206.

[6] Dunn, M.L., Wienecke, H.A., 1996. Green’s functions for transversely isotropic piezoelectric solids. Int. J. Solids Structures, 33(30):4571-4581.

[7] Leung, A.Y.T., Xu, X.S., 2005. A symplectic method for the exact homogeneous solutions of two-dimensional transversely isotropic piezoelectric media. J. Eng. Mech. (to be published).

[8] Zhong, W.X., 1995. A New Systematic Methodology for Theory of Elasticity. Dalian University of Technology Press, Dalian (in Chinese).

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