Symplectic analysis of plane problems of functionally graded piezoelectric materials

Mechanics of Materials

Volumn 41, Issue 12, 2009, Pages 1330-1339

  Zhao, L ^a   Chen, W Q ^a  

^a ZHEJIANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL METHOD; DIELECTRIC CONSTANTS; EIGEN-SOLUTIONS; EIGENVALUES; EIGENVECTORS; ELECTRIC DISPLACEMENT; EXPONENTIAL FORM; FUNCTIONALLY GRADED PIEZOELECTRIC MATERIAL; HAMILTONIAN MATRIX; HOMOGENEOUS MATERIALS; MATERIAL CONSTANT; MATERIAL INHOMOGENEITY; MATRIX; NUMERICAL RESULTS; OPERATOR MATRICES; PLANE PROBLEM; RIGID MOTIONS; SEPARATION OF VARIABLES; STATE EQUATIONS; SYMPLECTIC;

EIGENVALUES AND EIGENFUNCTIONS; ELASTIC CONSTANTS; ELECTRIC FIELDS; EQUATIONS OF MOTION; MATHEMATICAL OPERATORS; MEMS; PIEZOELECTRIC MATERIALS; PIEZOELECTRIC TRANSDUCERS; PIEZOELECTRICITY;

FUNCTIONALLY GRADED MATERIALS;

EID: 70349840418     PISSN: 01676636     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechmat.2009.09.001     Document Type: Article

References (26)

1. Borrelli A., Horgan C.O., and Patria M.C. Exponential decay of end effects in anti-plane shear for functionally graded piezoelectric materials. Proceedings of the Royal Society of London, Series A 460 (2004) 1193-1212
2. Borrelli A., Horgan C.O., and Patria M.C. Saint-Venant end effects for plane deformations of linear piezoelectric solids. International Journal of Solids and Structures 43 (2006) 943-956
3. Chen W.Q., and Ding H.J. Bending of functionally graded piezoelectric rectangular plates. Acta Mechanica Solida Sinica 13 (2000) 312-319
4. Chen W.Q., and Ding H.J. On free vibration of a functionally graded piezoelectric rectangular plate. Acta Mechanica 153 (2002) 207-216
5. Chen W.Q., Shioya T., and Ding H.J. The elasto-electric field for a rigid conical punch on a transversely isotropic piezoelectric half-space. Journal of Applied Mechanics 66 (1999) 764-771
6. Chen W.Q., Bian Z.G., Lu C.F., and Ding H.J. 3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid. International Journal of Solids and Structures 41 (2004) 947-964
7. Ding H.J., and Chen W.Q. Three-Dimensional Problems of Piezoelasticity (2001), Nova Science Publishers, New York
8. Ding H.J., Chen W.Q., and Xu R.Q. New state space formulations for transversely isotropic piezoelasticity with application. Mechanics Research Communications 27 (2000) 319-326
9. Ding H.J., Xu R.Q., Chi Y.W., and Chen W.Q. Free axisymmetric vibration of transversely isotropic piezoelectric circular plates. International Journal of Solids and Structures 36 (2000) 4629-4652
10. Gu, Q., 2007. An Analysis Method of Symplectic System for Mechanics of Piezoelectric Materials, Doctorial dissertation, Dalian University of Technology (in Chinese).
11. Gu Q., Xu X.S., and Leung A.Y.T. Application of Hamiltonian system for two-dimensional transversely isotropic piezoelectric media. Journal of Zhejiang University Science 6A 9 (2005) 915-921
12. He X.Q., Wang J.S., and Qin Q.H. Saint-Venant decay analysis of FGPM laminates and dissimilar piezoelectric laminates. Mechanics of Materials 39 (2007) 1053-1065
13. Huang G.Y., Wang Y.S., and Yu S.W. A new model for fracture analysis of functionally graded coatings under plane deformation. Mechanics of Materials 37 (2005) 507-516
14. Huang D.J., Ding H.J., and Chen W.Q. Analysis of functionally graded and laminated piezoelectric cantilever actuators subjected to constant voltage. Smart Materials and Structures 17 (2008) 1-11
15. Lee J.S., and Jiang L.Z. Exact electroelastic analysis of piezoelectric laminae via state space approach. International Journal of Solids and Structures 33 (1996) 977-990
16. Leung A.Y.T., Xu X.S., Gu Q., Leung C.T.O., and Zheng J.J. The boundary layer phenomena in two-dimensional transversely isotropic piezoelectric media by exact symplectic expansion. International Journal for Numerical Methods in Engineering 69 (2007) 2381-2408
17. Leung A.Y.T., Zheng J.J., Lim C.W., Zhang X.C., Xu X.S., and GU Q. A new symplectic approach for piezoelectric cantilever composite plates. Computers and Structures 86 (2008) 1865-1874
18. Nie G.J., and Zhong Z. Vibration analysis of functionally graded annular sectorial plates with simply supported radial edges. Composite Structures 84 (2008) 167-176
19. Ruan X.P., Stephen C.D., Ahmad S., and Chou T.W. Saint-Venant end effects in piezoceramic materials. International Journal of Solids and Structures 37 (2000) 2625-2637
20. Timoshenko S.P., and Goodier J.N. Theory of Elasticity (1970), McGraw-Hill, New York
21. Wang J.S., and Qin Q.H. A symplectic model for piezoelectric wedges and its application to analysis of electroelastic singularities. Philosophical Magazine 87 (2007) 225-251
22. Xu X.S., Zhong W.X., and Zhang H.W. The Saint-Venant problem and principle in elasticity. International Journal of Solids and Structures 34 22 (1997) 2815-2827
23. Xu X.S., Gu Q., Leung A.Y.T., and Zheng J.J. A symplectic eigensolution method in transversely isotropic piezoelectric cylindrical media. Journal of Zhejiang University Science 6A 9 (2005) 922-927
24. Xu X.S., Leung A.Y.T., Gu Q., Yang H., and Zheng J.J. 3D symplectic expansion for piezoelectric media. International Journal for Numerical Method in Engineering 74 (2008) 1848-1871
25. Yao W.A., and Zhong W.X. Symplectic Elasticity (2002), Higher Education Press, Beijing (in Chinese)
26. Zhong, W.X., 1995. A New Systematic Methodology for Theory of Elasticity, Publishing House of Dalian University of Technology, Dalian (in Chinese).