Abstract
This paper presents a symplectic method for two-dimensional transversely isotropic piezoelectric media with the aid of Hamiltonian system. A symplectic system is established directly by introducing dual variables and a complete space of eigensolutions is obtained. The solutions of the problem can be expressed by eigensolutions. Some solutions, which are local and are neglected usually by Saint Venant principle are shown. Curves of non-zero-eigenvalues and their eigensolutions are given by the numerical results.
Similar content being viewed by others
References
Chen, W.Q., 1999. On the application of potential theory in piezoelasticity.J. Appl. Mech.,66:808–810.
Chen, W.Q., Ding, H.J., 2004. Potential theory method for 3D crack and contact problems of multi-field coupled media: A survey.J. Zhejiang Univ. SCI,5(9):1009–1021.
Ding, H.J., Chen, W.Q., 2001. Three Dimensional Problems of Piezoelectricity. Nova Science Publishers, Inc., Hunington, New York.
Ding, H.J., Chen, B., Liang, J., 1996. General solutions for coupled equations for piezoelectric media.Int. J. Struct.,33:2283–2298.
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.
Dunn, M.L., Wienecke, H.A., 1996. Green’s functions for transversely isotropic piezoelectric solids.Int. J. Solids Struct.,33(30):4571–4581.
Sosa, H.A., Pak, Y.E., 1990. Three-dimensional eigenfunction analysis of a crack in a piezoelectric material.Int. J. Solids Struct.,26: 1–15.
Tzou, H.S., 1993. Piezoelectric Shells, Distributed Sensing and Control of continua. Solid Mechanics and Its Applications 19, Kluwer Academic Publishers.
Tzou, H.S., Smithmaitrie, P., Ding, J.H., 2002. Micro-sensor electromechanics and distributed signal analysis of piezo(electric)-elastic spherical shells.Mech. Systems. Signal Processing,16:185–199.
Xu, X.S., Zhong, W.X., Zhang, H.W., 1997, The Saint-Venant problem and principle in elasticity.Int. J. Solids Struct.,34:2815–2827.
Zhong, W.X., 1995. A New Systematic Methodology for Theory of Elasticity. Dalian University of Technology Press, Dalian (in Chinese).
Author information
Authors and Affiliations
Additional information
Project (Nos. 19902014 and 10272024) supported by the National Natural Science Foundation of China
Rights and permissions
About this article
Cite this article
Qian, G., Xin-sheng, X. & Leung Andrew, Y.T. Application of Hamiltonian system for two-dimensional transversely isotropic piezoelectric media. J Zheijang Univ Sci A 6, 915–921 (2005). https://doi.org/10.1631/jzus.2005.A0915
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.2005.A0915