Symplectic method for a piezoelectric cantilever beam

Proceedings of the 10th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp 2005

Volumn , Issue , 2005, Pages

  Leung, A Y T ^a   Zheng, J J ^a   Lim, C W ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Eigenvalue; Eigenvector; Hamiltonian system; Piezoelectric beam; Symplectic

Indexed keywords

APPLIED MATHEMATICS; CANONICAL SYSTEMS; EIGEN-SOLUTIONS; EIGEN-VALUE; HAMILTONIAN FORMULATIONS; HAMILTONIAN SYSTEM; HAMILTONIAN SYSTEMS; LENGTH-TO-WIDTH RATIO; LOADING CONDITION; LOCALIZED SOLUTIONS; MATHEMATICAL FOUNDATIONS; PIEZOELECTRIC BEAM; PIEZOELECTRIC CANTILEVER BEAMS; POLYNOMIAL METHODS; SAINT-VENANT PRINCIPLE; SCIENCE AND ENGINEERING; SEMI-INVERSE SOLUTION; SEPARATION OF VARIABLES; SPACE DIMENSIONS; SYMPLECTIC; SYMPLECTIC APPROACH; SYMPLECTIC GEOMETRY; SYMPLECTIC METHODS; TIME DIMENSION;

CANTILEVER BEAMS; COMPUTER AIDED ENGINEERING; EIGENVALUES AND EIGENFUNCTIONS; ENVIRONMENTAL ENGINEERING; MECHANICAL PROPERTIES; NANOCANTILEVERS; PIEZOELECTRICITY; POLYNOMIALS;

HAMILTONIANS;

EID: 80053401192     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (17)

1. H.J. Ding, W.Q. Chen, Z. Liu, "Solutions to equations of vibrations of spherical and cylindrical shells", Applied Mathematics and Mechanics, 16, 1-15, 1995.
2. H.J. Ding, W.Q. Chen, Y.M. Guo, "Free vibration of piezoelectric cylindrical shells filled with compressible fluid", International Journal of Solids and Structures, 33, 2025-2034, 1997.
3. H.J. Ding, W.Q. Chen, "Exact shell theory analysis of free vibrations of submerged thin spherical", International Journal of Solids and Structures, 35, 4381-4389, 1998.
4. H.J. Ding, W.Q. Chen, R.Q. Xu, "New state space formulations for transversely isotropic piezoelasticity with application", Mechanics Research Communications, 27, 319-326, 2000.
5. P.R. Heyliger, D.A. Saravanos, "Exact free-vibration analysis of laminated plates with embedded piezoelectric layers", Journal of Acoustical Society of America, 98, 1547-1557, 1995.
6. D.A. Saravanos, "Damped vibration of composite plates with passive piezoelectric-resisitor elements", Journal of Sound and Vibration, 221, 867-885, 1999.
7. T.R. Tauchert, "Piezothermoelastic behavior of a laminated plate", Journal of Thermal Stresses, 15, 25-37, 1992.
8. K. Xu, A.K. Noor, Y.Y Tang, "Three-dimensional solutions for coupled thermoelectroelastic response of multilayered plates" Computer Methods in Applied Mechanics and Engineering, 126, 355-371, 1995.
9. J.A. Mitchell, J.N. Reddy, "A refined hybrid plate theory for composite laminates with piezoelectric laminae", International Journal of Solids and Structures, 32, 2345-2367, 1995.
10. P.F. Pai, A.H. Nayfeh, "A refined nonlinear model of composite plates with integrated piezoelectric actuators and sensors", International Journal of Solids and Structures, 30, 1603-1630, 1993.
11. W.X. Zhong, "Plane elastic problem in strip domain and the Hamiltonian system", Journal of Dalian University of technology, 31:373-384, 1991.
12. A.Y.T. Leung, S.G. Mao, "Symplectic integration of an accurate beam finite element in non-linear vibration", Computers & structures, 54, 1135-1147, 1995.
13. A.Y.T. Leung, S.G. Mao, "A Symplectic galerkin method for non-linear vibration of beams and plates", Journal of Sound and Vibration, 183, 475-491, 1995.
14. A.Y.T. Leung, X.S. Xu, Q.A. Gu, "symplectic method for the exact homogeneous solutions of two-dimensional transversely isotropic piezoelectric media", Journal of Engineering Mechanics.(to be published)
15. Z.F. Shi, "General solution of a density functionally gradient piezoelectric cantilever and its applications", Smart Materials and Structures, 11, 122-129, 2002.
16. M.L. Dunn, M. Taya, "Electroelastic field concentrations in and around inhomogeneities in piezoelectric solids", Journal of Applied mechanics, 61, 474-475, 1994.
17. C.W. Lim, A.Y.T. Leung and C.W.H. Lau, "A variational energy approach for electromechanical analysis of thick piezoelectric actuator", First Symposium on Piezoelectricity, Acoustic Waves, and Device Applications, p60, 14-17 December 2004, Ningbo, Zhejiang, China.