Smart Structures and Systems

  • 제3권2호
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  • Pages.173-188
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  • 2007
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  • 1738-1584(pISSN)
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  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Analytical solutions for density functionally gradient magneto-electro-elastic cantilever beams

  • Jian, Aimin (Department of Civil Engineering, Zhejiang University, Department of Civil Engineering, Quzhou College) ;
  • Ding, Haojiang (Department of Civil Engineering, Zhejiang University)
  • 투고 : 2006.02.27
  • 심사 : 2006.12.12
  • 발행 : 2007.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

The general solution for two-dimensional magneto-electro-elastic media in terms of four harmonic displacement functions is proposed analytically. The expressions of specific solutions of magneto-electro-elastic plane problems with specific body forces are derived. Finally, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally gradient media, two kinds of beam problems with body forces depending only on the z or x coordinate are solved by the trial-and-error method.

키워드

참고문헌

  1. Chen, W. Q. and Lee, K. Y. (2003), "Alterative state space formulations for magneto-electric thermo- elasticity with transverse isotropy and the application to bending analysis of non-homogeneous plates", Int. J. Solids Struct., 40(21), 5689-5705. https://doi.org/10.1016/S0020-7683(03)00339-1
  2. Chen, W. Q., Lee, K. Y. and Ding, H. J. (2005), "On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates", J. Sound Vib., 279(1-2), 237-251. https://doi.org/10.1016/j.jsv.2003.10.033
  3. Ding, H. J. and Jiang, A. M. (2004), "A boundary integral formulation and solution for 2D problems in magneto-electro-elastic media", Computers & Struct., 82, 599-1607.
  4. Ding, H. J. and Jiang, A. M. (2003), "Fundamental solutions for transversely isotropic magneto-electro-elastic media and boundary integral formulation", Science in China(E), 46(6), 607-619.
  5. Ding, H. J., Wang, G. Q. and Chen, W. Q. (1997), "Fundamental solution for plane problem of piezoelectric materials", Science in China(E), 40(3), 331-336.
  6. Ding, H. J., Wang, G. Q. and Chen, W. Q. (1997), "General solution of plane problem of piezoelectric media expressed by "harmonic functions", Applied Mathematics and Mechanics, 18, 757-764. https://doi.org/10.1007/BF00763127
  7. Ding, H. J., Wang, G. Q. and Chen, W. Q. (1998), "Green's functions for piezoelectric half plane", Science in China(E), 41(1), 70-75.
  8. Ding, H. J., Wang, G. Q., Chen, W. Q. (1997), "Green's functions for a two-phase infinite piezoelectric plane", Proceedings of Royal Society of London(A), 453, 2241-57. https://doi.org/10.1098/rspa.1997.0120
  9. Heyliger, P. R. and Pan, E. (2004), "Static fields in magneto-electro-elastic laminates", AIAA Journal, 42(7), 1435-1443. https://doi.org/10.2514/1.9949
  10. Hou, P. F., Leung, Y. T. Andrew and Ding, H. J. (2003), "The elliptical Hertizan contact of transversely isotropic magneto-electro-elastic bodies", Int. J. Solids Struct., 40, 2833-2850. https://doi.org/10.1016/S0020-7683(02)00670-4
  11. Jiang, A. M. and Ding, H. J. (2005), "The analytical solutions to orthotropic cantilever beams(II): Solutions for density functionally graded beams", J. Zhejiang Univ. SCI., 6A(3), 155-158. https://doi.org/10.1631/jzus.2005.A0155
  12. Jiang, A. M. and Ding, H. J. (2004), "Analytical solutions to magneto-electro-elastic beams", Structural Engineering and Mechanics, 18(2), 195-209. https://doi.org/10.12989/sem.2004.18.2.195
  13. Jiang, A. M. and Ding, H. J. (2005), "The analytical solutions to orthotropic cantilever beams(I): Subjected to surface forces", J. Zhejiang Univ. SCI., 6A(2), 126-131. https://doi.org/10.1631/jzus.2005.A0126
  14. Pan, E. (2001), "Exact solution for simply supported and multilayered magneto-electro-elastic plates", ASME J. App. Mech., 68, 608-618. https://doi.org/10.1115/1.1380385
  15. Pan, E. (2002), "Three-dimensional Green's function in anisotropic magneto-electro-elastic bimaterials", Z. angew. Math. Phys., 53, 815-838. https://doi.org/10.1007/s00033-002-8184-1
  16. Pan, E. and Heyliger, P. R. (2002), "Free vibrations of simply supported and multilayered magneto- electroelastic plates", J. Sound and Vib., 252, 429-442. https://doi.org/10.1006/jsvi.2001.3693
  17. Pan, E. and Heyliger, P. R. (2003), "Exact solutions for magneto-electro-elastic laminates in cylindrical bending", Int. J. Solids and Struct., 40(24), 6859-6876. https://doi.org/10.1016/j.ijsolstr.2003.08.003
  18. Shi, Z. F. (2001), "Analysis of a piezoelectric cantilever with non-uniform body force", 13th international conference on composite materials. June25-29, Beijing, P.R. China.
  19. Shi, Z. F. (2002), "General solution of a density functionally gradient piezoelectric cantilever and its applications", Smart Mater. Struct. 11, 122-129. https://doi.org/10.1088/0964-1726/11/1/314
  20. Shi, Z. F., Chen, Y. (2004), "Functionally graded piezoelectric cantilever beam under load", Archive of Applied Mechanics, 74(3-4), 237-247. https://doi.org/10.1007/s00419-004-0346-5
  21. Sosa, H. A. and Castro, M. A. (1994), "On concentrated loads at the boundary of a piezoelectric half-plane", J. Mech. Phys. Solids, 42(7), 1105-1122. https://doi.org/10.1016/0022-5096(94)90062-0
  22. Wang, J. G., Chen, L. F. and Fang, S. S. (2003), "State vector approach to analysis of multi-layered magnetoelectro-elastic plates", Int. J. Solids and Struct., 40, 1669-1680. https://doi.org/10.1016/S0020-7683(03)00027-1
  23. Wang, X. and Shen, Y. P. (2002), "The general solution of three-dimensional problems in magneto-/electroelastic media", Int. J. Eng. Sci., 40, 1069-1080. https://doi.org/10.1016/S0020-7225(02)00006-X
  24. Wang, X., Shen, Y. P. (2003), "Inclusion of arbitrary shape in magneto-electro-elastic composite materials", Int. J. Eng. Sci., 41, 85-102. https://doi.org/10.1016/S0020-7225(02)00110-6
  25. Yang, D. Q., Liu, Z. X. (2003), "Analytical solution for bending of a piezoelectric cantilever beam under an end load", Chinese Quarterly of Mechanics (in Chinese), 24(3), 327-333.

피인용 문헌

  1. Free vibration and static analysis of functionally graded skew magneto-electro-elastic plate vol.21, pp.4, 2007, https://doi.org/10.12989/sss.2018.21.4.493