Table of Contents Author Guidelines Submit a Manuscript
Advances in Acoustics and Vibration
Volume 2012, Article ID 189376, 16 pages
http://dx.doi.org/10.1155/2012/189376
Research Article

Dynamical Analysis of Long Fiber-Reinforced Laminated Plates with Elastically Restrained Edges

1INIQUI-CONICET, Facultad de Ingeniería, Universidad Nacional de Salta, Avenue Bolivia 5150, 4400 Salta, Argentina
2International Center for Numerical Method in Engineering, (CIMNE) Technical University of Catalonia-Barcelona Tech (UPC), Edif. C1, Campus Nord, Jordi Girona 1-3, 08034 Barcelona, Spain

Received 30 December 2010; Revised 7 August 2011; Accepted 14 September 2011

Academic Editor: Kok Keong Choong

Copyright © 2012 Liz G. Nallim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. Reissner, “On transverse bending of plates, including the effect of transverse shear deformation,” International Journal of Solids and Structures, vol. 11, no. 5, pp. 569–576, 1975. View at Google Scholar · View at Scopus
  2. R. D. Mindlin, “Influences of rotatory inertia and shear inflexural motion of isotropic, elastic plates,” Journal of Applied Mechanics, vol. 18, pp. 1031–1036, 1951. View at Google Scholar
  3. H. R. H. Kabir, “On the frequency response of moderately thick simply supported rectangular plates with arbitrary lamination,” International Journal of Solids and Structures, vol. 36, no. 15, pp. 2285–2301, 1999. View at Google Scholar · View at Scopus
  4. K. M. Liew, “Solving the vibation of thick symmetric laminates by Reissner/Mindlin plate theory and the p-Ritz method,” Journal of Sound and Vibration, vol. 198, no. 3, pp. 343–360, 1996. View at Publisher · View at Google Scholar · View at Scopus
  5. J. W. Shi, A. Nakatani, and H. Kitagawa, “Vibration analysis of fully clamped arbitrarily laminated plate,” Composite Structures, vol. 63, no. 1, pp. 115–122, 2004. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Aydogdu and T. Timarci, “Vibration analysis of cross-ply laminated square plates with general boundary conditions,” Composites Science and Technology, vol. 63, no. 7, pp. 1061–1070, 2003. View at Publisher · View at Google Scholar · View at Scopus
  7. L. Liu, L. P. Chua, and D. N. Ghista, “Mesh-free radial basis function method for static, free vibration and buckling analysis of shear deformable composite laminates,” Composite Structures, vol. 78, no. 1, pp. 58–69, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. G. R. Liu, X. Zhao, K. Y. Dai, Z. H. Zhong, G. Y. Li, and X. Han, “Static and free vibration analysis of laminated composite plates using the conforming radial point interpolation method,” Composites Science and Technology, vol. 68, no. 2, pp. 354–366, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. J. Wang, K. M. Liew, M. J. Tan, and S. Rajendran, “Analysis of rectangular laminated composite plates via FSDT meshless method,” International Journal of Mechanical Sciences, vol. 44, no. 7, pp. 1275–1293, 2002. View at Publisher · View at Google Scholar · View at Scopus
  10. K. S. Numayr, R. H. Haddad, and M. A. Haddad, “Free vibration of composite plates using the finite difference method,” Thin-Walled Structures, vol. 42, no. 3, pp. 399–414, 2004. View at Publisher · View at Google Scholar · View at Scopus
  11. W. Lanhe, L. Hua, and W. Daobin, “Vibration analysis of generally laminated composite plates by the moving least squares differential quadrature method,” Composite Structures, vol. 68, no. 3, pp. 319–330, 2005. View at Publisher · View at Google Scholar · View at Scopus
  12. P. Ribeiro, “First-order shear deformation, p-version, finite element for laminated plate nonlinear vibrations,” AIAA Journal, vol. 43, no. 6, pp. 1371–1379, 2005. View at Google Scholar · View at Scopus
  13. A. J. M. Ferreira and G. E. Fasshauer, “Analysis of natural frequencies of composite plates by an RBF-pseudospectral method,” Composite Structures, vol. 79, no. 2, pp. 202–210, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. P. Malekzadeh and S. A. Shahpari, “Free vibration analysis of variable thickness thin and moderately thick plates with elastically restrained edges by DQM,” Thin-Walled Structures, vol. 43, no. 7, pp. 1037–1050, 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. F. Ohya, M. Ueda, T. Uchiyama, and M. Kikuchi, “Free vibration analysis by the superposition method of rectangular Mindlin plates with internal columns resting on uniform elastic edge supports,” Journal of Sound and Vibration, vol. 289, no. 1-2, pp. 1–24, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. D. Zhou, “Vibrations of Mindlin rectangular plates with elastically restrained edges using static Timoshenko beam functions with the Rayleigh-Ritz method,” International Journal of Solids and Structures, vol. 38, no. 32-33, pp. 5565–5580, 2001. View at Publisher · View at Google Scholar · View at Scopus
  17. K. Khorshidi, “Vibro-acoustic analysis of Mindlin rectangular plates resting on an elastic foundation,” Scientia Iranica, vol. 18, no. 1, pp. 60–69, 2001. View at Google Scholar
  18. L. H. Wu and Y. Lu, “Free vibration analysis of rectangular plates with internal columns and uniform elastic edge supports by pb-2 Ritz method,” International Journal of Mechanical Sciences, vol. 53, no. 7, pp. 494–504, 2011. View at Google Scholar
  19. G. Y. Jin, H. Chen, J. T. Du, T. J. Yang, and W. Y. Li, “The Influence of edge restraining stiffness on the transverse vibrations of rectangular plate structures,” Journal of Marine Science and Application, vol. 9, no. 4, pp. 393–402, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. A. R. Setoodeh and G. Karami, “A solution for the vibration and buckling of composite laminates with elastically restrained edges,” Composite Structures, vol. 60, no. 3, pp. 245–253, 2003. View at Publisher · View at Google Scholar · View at Scopus
  21. G. Karami, P. Malekzadeh, and S. R. Mohebpour, “DQM free vibration analysis of moderately thick symmetric laminated plates with elastically restrained edges,” Composite Structures, vol. 74, no. 1, pp. 115–125, 2006. View at Publisher · View at Google Scholar · View at Scopus
  22. A. S. Ashour, “Vibration of angle-ply symmetric laminated composite plates with edges elastically restrained,” Composite Structures, vol. 74, no. 3, pp. 294–302, 2006. View at Publisher · View at Google Scholar · View at Scopus
  23. L. G. Nallim and R. O. Grossi, “Vibration of angle-ply symmetric laminated composite plates with edges elastically restrained,” Composite Structures, vol. 81, no. 1, pp. 80–83, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. S. Chakraverty and M. Petyt, “Natural frequencies for free vibration of nonhomogeneous elliptic and circular plates using two-dimensional orthogonal polynomials,” Applied Mathematical Modelling, vol. 21, no. 7, pp. 399–417, 1997. View at Google Scholar · View at Scopus
  25. B. Singh and S. Chakraverty, “Flexural vibration of skew plates using boundary characteristic orthogonal polynomials in two variables,” Journal of Sound and Vibration, vol. 173, no. 2, pp. 157–178, 1994. View at Publisher · View at Google Scholar · View at Scopus
  26. S. Chakraverty, R. B. Bhat, and I. Stiharu, “Free vibration of annular elliptic plates using boundary characteristic orthogonal polynomials as shape functions in the Rayleigh-Ritz method,” Journal of Sound and Vibration, vol. 241, no. 3, pp. 524–539, 2001. View at Publisher · View at Google Scholar · View at Scopus
  27. S. T. Chow, K. M. Liew, and K. Y. Lam, “Transverse vibration of symmetrically laminated rectangular composite plates,” Composite Structures, vol. 20, no. 4, pp. 213–226, 1992. View at Google Scholar · View at Scopus
  28. H. Altenbach, J. Altenbach, and W. Kisssing, Mechanics of Composite Structural Elements, Springer, Berlin, Germany, 2004.
  29. T. Mori and K. Tanaka, “Average stress in matrix and average elastic energy of materials with misfitting inclusions,” Acta Metallurgica, vol. 21, no. 5, pp. 571–574, 1973. View at Google Scholar · View at Scopus
  30. P. D. Soden, M. J. Hinton, and A. S. Kaddour, “Lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates,” Composites Science and Technology, vol. 58, no. 7, pp. 1011–1022, 1998. View at Publisher · View at Google Scholar
  31. A. Alibeigloo, M. Shakeri, and M. R. Kari, “Free vibration analysis of antisymmetric laminated rectangular plates with distributed patch mass using third-order shear deformation theory,” Ocean Engineering, vol. 35, no. 2, pp. 183–190, 2008. View at Publisher · View at Google Scholar · View at Scopus
  32. J. N. Reddy, “A simple higher-order theory for laminated composite plates,” ASME Journal of Applied Mechanics, vol. 51, no. 4, pp. 745–752, 1984. View at Google Scholar · View at Scopus
  33. J. D. Eshelby, “The determination of the elastic field of an ellipsoidal inclusion and related problems,” Proceedings of the Royal Society, vol. 241, pp. 376–396, 1957. View at Google Scholar
  34. G. P. Tandon and G. J. Weng, “The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites,” Polymer Composites, vol. 5, no. 4, pp. 327–333, 1984. View at Google Scholar
  35. J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, Fla, USA, 2nd edition, 2003.
  36. J. M. Whitney, Structural Analysis of Laminated Anisotropic Plates, Technomic Publishing Co., Lancaster, Pa, USA, 1987.
  37. L. G. Nallim and R. O. Grossi, “On the use of orthogonal polynomials in the study of anisotropic plates,” Journal of Sound and Vibration, vol. 264, no. 5, pp. 1201–1207, 2003. View at Publisher · View at Google Scholar · View at Scopus
  38. L. G. Nallim and S. Oller, “An analytical-numerical approach to simulate the dynamic behaviour of arbitrarily laminated composite plates,” Composite Structures, vol. 85, no. 4, pp. 311–325, 2008. View at Publisher · View at Google Scholar · View at Scopus
  39. R. B. Bhat, “Plate deflection using orthogonal polynomials,” Journal of Engineering Mechanics, vol. 101, no. 11, pp. 1301–1309, 1985. View at Google Scholar · View at Scopus
  40. N. M. Auciello and A. Ercolano, “A general solution for dynamic response of axially loaded non-uniform Timoshenko beams,” International Journal of Solids and Structures, vol. 41, no. 18-19, pp. 4861–4874, 2004. View at Publisher · View at Google Scholar · View at Scopus