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Mathematical Problems in Engineering
Volume 2010, Article ID 547956, 14 pages
http://dx.doi.org/10.1155/2010/547956
Research Article

Free Vibration of Layered Circular Cylindrical Shells of Variable Thickness Using Spline Function Approximation

Department of Naval Architecture & Ocean Engineering, Inha University, 253 Yonghyun-dong, Nam-gu, Incheon 402-751, Republic of Korea

Received 2 February 2010; Revised 9 July 2010; Accepted 10 August 2010

Academic Editor: Paulo Batista Gonçalves

Copyright © 2010 K. K. Viswanathan 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. H. Baker and G. Herrmann, “Vibrations of orthotropic cylindrical sandwich shells under initial stress,” AIAA Journal, vol. 29, pp. 963–975, 1966. View at Google Scholar · View at Zentralblatt MATH
  2. K. R. Sivadas and N. Ganesan, “Free vibration of circular cylindrical shells with axially varying thickness,” Journal of Sound and Vibration, vol. 147, no. 1, pp. 73–85, 1991. View at Publisher · View at Google Scholar · View at Scopus
  3. R. F. Tonin and D. A. Bies, “Free vibration of circular cylinders of variable thickness,” Journal of Sound and Vibration, vol. 62, no. 2, pp. 165–180, 1979. View at Publisher · View at Google Scholar · View at Scopus
  4. S. Takahashi, K. Suzuki, T. Kosawada, and E. Anzai, “Vibration of cylindrical shells with variable thickness,” Bulletin of Japan Society of Mechanical Engineers, vol. 24, pp. 1826–1836, 1981. View at Google Scholar
  5. K. Suzuki, E. Anzai, and S. Takahashi, “Vibration of cylindrical shells with varying thickness,” Bulletin of Japan Society of Mechanical Engineers, vol. 25, pp. 1108–1119, 1982. View at Google Scholar
  6. K. R. Sivadas and N. Ganesan, “Axisymmetric vibration analysis of thick cylindrical shell with variable thickness,” Journal of Sound and Vibration, vol. 160, no. 3, pp. 387–400, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. E. Hinton, M. Özakça, and N. V. R. Rao, “Free vibration analysis and shape optimization of variable thickness plates, prismatic folded plates and curved shells. Part 1: finite strip formulation,” Journal of Sound and Vibration, vol. 181, no. 4, pp. 553–566, 1995. View at Publisher · View at Google Scholar · View at Scopus
  8. G. Sun, P. N. Bennett, and F. W. Williams, “An investigation on fundamental frequencies of laminated circular cylinders given by shear deformable finite elements,” Journal of Sound and Vibration, vol. 205, no. 3, pp. 265–273, 1997. View at Publisher · View at Google Scholar · View at Scopus
  9. X. M. Zhang, “Vibration analysis of cross-ply laminated composite cylindrical shells using the wave propagation approach,” Applied Acoustics, vol. 62, no. 11, pp. 1221–1228, 2001. View at Publisher · View at Google Scholar · View at Scopus
  10. W. Hufenbach, C. Holste, and L. Kroll, “Vibration and damping behaviour of multi-layered composite cylindrical shells,” Composite Structures, vol. 58, no. 1, pp. 165–174, 2002. View at Publisher · View at Google Scholar · View at Scopus
  11. T. Sakiyama, X. X. Hu, H. Matsuda, and C. Morita, “Vibration of twisted and curved cylindrical panels with variable thickness,” Journal of Sound and Vibration, vol. 254, no. 3, pp. 481–502, 2002. View at Publisher · View at Google Scholar · View at Scopus
  12. T. Tsuiji and T. Sueoka, “Free vibrations of twisted thin cylindrical panels (numerical analysis by using the Rayleigh-Ritz method),” Transactions of the Japan Society of Mechanical Engineers, Part C, vol. 55, no. 514, pp. 1325–1329, 1989. View at Google Scholar · View at Scopus
  13. S. Tizzi, “A Ritz procedure for optimisation of cylindrical shells, formed by a nearly symmetric and balanced angle-ply composite laminate, with fixed minimum frequency,” Computers & Structures, vol. 84, no. 31-32, pp. 2159–2173, 2006. View at Publisher · View at Google Scholar · View at Scopus
  14. M. H. Toorani and A. A. Lakis, “Free vibrations of non-uniform composite cylindrical shells,” Nuclear Engineering and Design, vol. 236, no. 17, pp. 1748–1758, 2006. View at Publisher · View at Google Scholar · View at Scopus
  15. T. Mizusawa and H. Kito, “Vibration of cross-ply laminated cylindrical panels by the spline strip method,” Computers and Structures, vol. 57, no. 2, pp. 253–265, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. W. G. Bickley, “Piecewise cubic interpolation and two-point boundary problems,” Computer Journal, vol. 11, pp. 206–208, 1968. View at Google Scholar · View at Zentralblatt MATH
  17. K. K. Viswanathan and P. V. Navaneethakrishnan, “Free vibration study of layered cylindrical shells by collocation with splines,” Journal of Sound and Vibration, vol. 260, no. 5, pp. 807–827, 2003. View at Publisher · View at Google Scholar · View at Scopus
  18. K. K. Viswanathan and K. S. Kim, “Free vibration of antisymmetric angle-ply-laminated plates including transverse shear deformation: spline method,” International Journal of Mechanical Sciences, vol. 50, no. 10-11, pp. 1476–1485, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. K. K. Viswanathan, K. S. Kim, J. H. Lee, H. S. Koh, and J. B. Lee, “Free vibration of multi-layered circular cylindrical shell with cross-ply walls, including shear deformation by using spline function method,” Journal of Mechanical Science and Technology, vol. 22, no. 11, pp. 2062–2075, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. S. A. Ambartsumyan, “Theory of anisotropic shells,” Tech. Rep. NASA TTF-118, 1964. View at Google Scholar