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Modelling and Simulation in Engineering
Volume 2012 (2012), Article ID 492415, 8 pages
http://dx.doi.org/10.1155/2012/492415
Research Article

A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams

Department of Aerospace Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, Canada M5B 2K3

Received 31 March 2011; Accepted 30 September 2011

Academic Editor: Jing-song Hong

Copyright © 2012 Nicholas H. Erdelyi and Seyed M. Hashemi. 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. J. Wang, Y. Liu, and J. Gibby, “Vibrations of split beams,” Journal of Sound and Vibration, vol. 84, no. 4, pp. 491–502, 1982. View at Scopus
  2. P. Mujumdar and S. Suryanarayan, “Flexural vibrations of beams with delaminations,” Journal of Sound and Vibration, vol. 125, no. 3, pp. 441–461, 1988. View at Scopus
  3. S. M. Hashemi and A. Roach, “A Dynamic Finite Element for vibration analysis of composite circular tubes,” in Proceedings of the 10th International Conference on Civil, Structural and Environmental Engineering Computing (Civil-Comp '05), B. H. V. Topping, Ed., Civil-Comp Press, Rome, Italy, August-September 2005.
  4. S. M. Hashemi and S. Borneman, “Doubly-coupled vibrations of nonuniform composite wings: a dynamic finite element,” in Mathematical Problems in Engineering, Aerospace and Sciences, Vol. 5, S. Sivasundaram, Ed., Cambridge Scientific, 2011, paper no. 18.
  5. S. M. Hashemi and A. Roach, “A dynamic finite element for the free vibration analysis of extension-torsion coupled composite beams,” Mathematics in Engineering, Science and Aerospace, vol. 1, no. 3, pp. 221–239, 2010.
  6. J. Lee, “Free vibration analysis of delaminated composite beams,” Computers and Structures, vol. 74, no. 2, pp. 121–129, 2000. View at Publisher · View at Google Scholar · View at Scopus
  7. C. N. Della and D. Shu, “Vibration of delaminated multilayer beams,” Composites Part B, vol. 37, no. 2-3, pp. 227–236, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. C. N. Della and D. Shu, “Free vibration analysis of multiple delaminated beams under axial compressive load,” Journal of Reinforced Plastics and Composites, vol. 28, no. 11, pp. 1365–1381, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. N. Erdelyi and S. M. Hashemi, “Free vibration analysis of delaminated layered beams: a Dynamic Finite Element (DFE) technique,” in Proceedings of the 8th Joint Canada-Japan Workshop on Composite Materials, p. 10, Montreal, Canada, July 2010.
  10. J. R. Banerjee and F. W. Williams, “Coupled bending-torsional dynamic stiffness matrix of an axially loaded timoshenko beam element,” International Journal of Solids and Structures, vol. 31, no. 6, pp. 749–762, 1994. View at Scopus
  11. J. R. Banerjee and F. W. Williams, “Free vibration of composite beams—an exact method using symbolic computation,” Journal of Aircraft, vol. 32, no. 3, pp. 636–642, 1995.
  12. J. R. Banerjee, “Free vibration of sandwich beams using the dynamic stiffness method,” Computers and Structures, vol. 81, no. 18-19, pp. 1915–1922, 2003. View at Publisher · View at Google Scholar · View at Scopus
  13. J. R. Banerjee and A. J. Sobey, “Dynamic stiffness formulation and free vibration analysis of a three-layered sandwich beam,” International Journal of Solids and Structures, vol. 42, no. 8, pp. 2181–2197, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. J. R. Banerjee, C. W. Cheung, R. Morishima, M. Perera, and J. Njuguna, “Free vibration of a three-layered sandwich beam using the dynamic stiffness method and experiment,” International Journal of Solids and Structures, vol. 44, no. 22-23, pp. 7543–7563, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. J. R. Banerjee, H. Su, and C. Jayatunga, “A dynamic stiffness element for free vibration analysis of composite beams and its application to aircraft wings,” Computers and Structures, vol. 86, no. 6, pp. 573–579, 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. J. R. Banerjee, “Dynamic stiffness formulation for structural elements: a general approach,” Computers and Structures, vol. 63, no. 1, pp. 101–103, 1997. View at Scopus
  17. W. H. Wittrick and F. W. Williams, “A general algorithm for computing natural frequencies of elastic structures,” Quarterly Journal of Mechanics and Applied Mathematics, vol. 24, no. 3, pp. 263–284, 1971. View at Publisher · View at Google Scholar · View at Scopus
  18. K. Wang, D. J. Inman, and C. R. Farrar, “Modeling and analysis of a cracked composite cantilever beam vibrating in coupled bending and torsion,” Journal of Sound and Vibration, vol. 284, no. 1-2, pp. 23–49, 2005. View at Publisher · View at Google Scholar · View at Scopus
  19. K. Wang, Vibration analysis of cracked composite bending-torsion beams for damage diagnosis, Ph.D. dissertation, Department of Mechanical Engineering, Virginia Tech, Blacksburg, Va, USA, 2004, http://scholar.lib.vt.edu/theses/available/etd-12032004-110007/.
  20. S. R. Borneman, S. M. Hashemi, and H. Alighanbari, “Vibration analysis of doubly coupled cracked composite beams: an exact dynamic stiffness matrix,” International Review of Aerospace Engineering, vol. 1, no. 3, pp. 298–309, 2008.
  21. N. Erdelyi and S. M. Hashemi, “An exact dynamic stiffness matrix (DSM) formulation for free vibration analysis of delaminated beams,” in Proceedings of the 8th Joint Canada-Japan Workshop on Composite Materials, p. 10, Montreal, Canada, July 2010.
  22. K.-J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice Hall, 1982.
  23. N. Erdelyi, Development of a dynamic finite element model to describe the vibration of delaminated composite beams, Ph.D. thesis, Department of Aerospace Engineering, Ryerson University, Toronto, Canada, 2010.
  24. S. M. Hashemi, Free vibrational analysis of rotating beam-like structures: a dynamic finite element approach, Ph.D. thesis, Department of Mechanical Engineering, Laval University, Québec, Canada, 1998.
  25. F. W. Williams and W. H. Wittrick, “An automatic computational procedure for calculating natural frequencies of skeletal structures,” International Journal of Mechanical Sciences, vol. 12, no. 9, pp. 781–791, 1970. View at Scopus
  26. P. Swannell, “The automatic computation of natural frequencies of structural frames using an exact matrix technique,” in Proceedings of the 1973 Tokyo Seminar on Theory and Practice in Finite Element Strcutural Analysis, pp. 289–301, 1973.
  27. C. H. Roche and M. L. Accorsi, “A new finite element for global modeling of delaminations in laminated beams,” Finite Elements in Analysis and Design, vol. 31, no. 2, pp. 165–177, 1998. View at Scopus