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Shock and Vibration
Volume 2016 (2016), Article ID 3707658, 14 pages
http://dx.doi.org/10.1155/2016/3707658
Research Article

On the Finite Element Free Vibration Analysis of Delaminated Layered Beams: A New Assembly Technique

Nicholas H. Erdelyi and Seyed M. Hashemi

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

Received 20 July 2015; Revised 16 October 2015; Accepted 21 October 2015

Academic Editor: Longjun Dong

Copyright © 2016 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. S. Benmedakhene, M. Kenane, and M. L. Benzeggagh, “Initiation and growth of delamination in glass/epoxy composites subjected to static and dynamic loading by acoustic emission monitoring,” Composites Science and Technology, vol. 59, no. 2, pp. 201–208, 1999. View at Publisher · View at Google Scholar · View at Scopus
  2. X. Zhuang and X. Yan, “Investigation of damage mechanisms in self-reinforced polyethylene composites by acoustic emission,” Composites Science and Technology, vol. 66, no. 3-4, pp. 444–449, 2006. View at Publisher · View at Google Scholar · View at Scopus
  3. D. Crivelli, M. Guagliano, M. Eaton et al., “Localisation and identification of fatigue matrix cracking and delamination in a carbon fibre panel by acoustic emission,” Composites Part B: Engineering, vol. 74, pp. 1–12, 2015. View at Publisher · View at Google Scholar · View at Scopus
  4. A. Szekrényes, “A special case of parametrically excited systems: free vibration of delaminated composite beams,” European Journal of Mechanics—A/Solids, vol. 49, pp. 82–105, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. Z. Juhász and A. Szekrényes, “Estimation of local delamination buckling in orthotropic composite plates using Kirchhoff plate finite elements,” Mathematical Problems in Engineering, vol. 2015, Article ID 749607, 14 pages, 2015. View at Publisher · View at Google Scholar
  6. J. T. S. Wang, Y. Y. Liu, and J. A. Gibby, “Vibrations of split beams,” Journal of Sound and Vibration, vol. 84, no. 4, pp. 491–502, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. P. M. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. A. Szekrényes, “Coupled flexural-longitudinal vibration of delaminated composite beams with local stability analysis,” Journal of Sound and Vibration, vol. 333, no. 20, pp. 5141–5164, 2014. View at Publisher · View at Google Scholar · View at Scopus
  9. J. J. Tracy and G. C. Pardoen, “Effect of delamination on the natural frequencies of composite laminates,” Journal of Composite Materials, vol. 23, no. 12, pp. 1200–1216, 1989. View at Publisher · View at Google Scholar
  10. M.-H. H. Shen and J. E. Grady, “Free vibrations of delaminated beams,” AIAA Journal, vol. 30, no. 5, pp. 1361–1370, 1992. View at Publisher · View at Google Scholar · View at Scopus
  11. W. Lestari and S. Hanagud, “Health monitoring of structures: multiple delamination dynamics in composite beams,” Report for American Institute of Aeronautics and Astronautics AIAA-99-1509, American Institute of Aeronautics and Astronautics, Reston, Va, USA, 1999. View at Google Scholar
  12. L. Brandinelli and R. Massabò, “Free vibrations of delaminated beam-type structures with crack bridging,” Composite Structures, vol. 61, no. 1-2, pp. 129–142, 2003. View at Publisher · View at Google Scholar · View at Scopus
  13. D. Shu and H. Fan, “Free vibration of bimaterial split beam,” Composites Part B: Engineering, vol. 27, no. 1, pp. 79–84, 1996. View at Publisher · View at Google Scholar · View at Scopus
  14. D. Shu, “Vibration of sandwich beams with double delaminations,” Composites Science and Technology, vol. 54, no. 1, pp. 101–109, 1995. View at Publisher · View at Google Scholar · View at Scopus
  15. H. Hein, “The influence of delamination on free vibrations of composite beams on Pasternak soil,” Proceedings of the Estonian Academy of Sciences, Physics, Mathematics, vol. 55, no. 4, pp. 220–234, 2006. View at Google Scholar
  16. S. H. Jian and C. Hwu, “Free vibration of delaminated composite sandwich beams,” AIAA Journal, vol. 33, no. 10, pp. 1911–1918, 1995. View at Publisher · View at Google Scholar · View at Scopus
  17. J. Lee, “Free vibration analysis of delaminated composite beams,” Computers & Structures, vol. 74, no. 2, pp. 121–129, 2000. View at Publisher · View at Google Scholar · View at Scopus
  18. S. Lee, T. Park, and G. Z. Voyiadjis, “Free vibration analysis of axially compressed laminated composite beam-columns with multiple delaminations,” Composites Part B: Engineering, vol. 33, no. 8, pp. 605–617, 2002. View at Publisher · View at Google Scholar · View at Scopus
  19. S. Lee, T. Park, and G. Z. Voyiadjis, “Vibration analysis of multi-delaminated beams,” Composites Part B: Engineering, vol. 34, no. 7, pp. 647–659, 2003. View at Publisher · View at Google Scholar · View at Scopus
  20. ANSYS, Academic Research, Release 13.0, Help System, ANSYS, Canonsburg, Pa, USA, 2009.
  21. A. R. Ghorbanzad, Free vibration analysis of layered beams with delamination damage—an ANSYS-based FEM investigation [M.S. thesis], Department of Aerospace Engineering, Ryerson University, Toronto, Canada, 2012.
  22. 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.
  23. 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.
  24. J. R. Banerjee, “Dynamic stiffness formulation for structural elements: a general approach,” Computers & Structures, vol. 63, no. 1, pp. 101–103, 1997. View at Publisher · View at Google Scholar · View at Scopus
  25. 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 Zentralblatt MATH · View at Scopus
  26. 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.
  27. N. H. Erdelyi and S. M. Hashemi, “A dynamic stiffness element for free vibration analysis of delaminated layered beams,” Modelling and Simulation in Engineering, vol. 2012, Article ID 492415, 8 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  28. C. N. Della and D. Shu, “Vibration of delaminated multilayer beams,” Composites Part B: Engineering, vol. 37, no. 2-3, pp. 227–236, 2006. View at Publisher · View at Google Scholar · View at Scopus
  29. C. N. Della and D. Shu, “Free vibration analysis of composite beams with overlapping delaminations,” European Journal of Mechanics—A/Solids, vol. 24, no. 3, pp. 491–503, 2005. View at Publisher · View at Google Scholar · View at Scopus
  30. C. N. Della and D. Shu, “Vibration of delaminated composite laminates: a review,” Applied Mechanics Reviews, vol. 60, no. 1–6, pp. 1–20, 2007. View at Publisher · View at Google Scholar · View at Scopus
  31. 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
  32. K.-J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, 1982.
  33. S. M. Hashemi and E. J. Adique, “A quasi-exact dynamic finite element for free vibration analysis of sandwich beams,” Applied Composite Materials, vol. 17, no. 2, pp. 259–269, 2010. View at Publisher · View at Google Scholar · View at Scopus
  34. S. M. Hashemi and A. Roach, “Dynamic finite element analysis of extensional-torsional coupled vibration in nonuniform composite beams,” Applied Composite Materials, vol. 18, no. 6, pp. 521–538, 2011. View at Publisher · View at Google Scholar · View at Scopus
  35. 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, S. Sivasundaram, Ed., vol. 5, pp. 141–152, Cambridge Scientific Publishers, 2011. View at Google Scholar
  36. 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 Publisher · View at Google Scholar · View at Scopus
  37. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus