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Advances in Materials Science and Engineering
Volume 2016, Article ID 1509384, 19 pages
http://dx.doi.org/10.1155/2016/1509384
Research Article

Bifurcation Study of Thin Plate with an All-Over Breathing Crack

Beijing University of Technology, No. 100, Pingleyuan, Chaoyang District, Beijing, China

Received 17 June 2016; Revised 17 September 2016; Accepted 16 October 2016

Academic Editor: Ying Li

Copyright © 2016 Lihua Chen 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. A. D. Dimarogonas, “Vibration of cracked structures: a state of the art review,” Engineering Fracture Mechanics, vol. 55, no. 5, pp. 831–857, 1996. View at Publisher · View at Google Scholar · View at Scopus
  2. J. R. Rice and N. Levy, “The part-through surface crack in an elastic plate,” Journal of Applied Mechanics, vol. 3, pp. 183–194, 1972. View at Google Scholar · View at Scopus
  3. H. P. Lee, S. P. Lim, and S. T. Chow, “Prediction of natural frequencies of cracked isotropic and orthotropic composite plate,” in Proceedings of the International Conference on Computational Engineering Mechanics, pp. 632–648, Beijing, China, 1987.
  4. S. E. Khadem and M. Rezaee, “An analytical approach for obtaining the location and depth of an all-over part-through crack on externally in-plane loaded using vibration analysis,” Journal of Sound and Vibration, vol. 230, pp. 291–308, 1999. View at Google Scholar
  5. S. E. Khadem and M. Rezaee, “Introduction of modified comparison functions for vibration analysis of a rectangular cracked plate,” Journal of Sound and Vibration, vol. 236, no. 2, pp. 245–258, 2000. View at Publisher · View at Google Scholar · View at Scopus
  6. Sh. Hosseini-Hashemi, Gh. Heydar Roohi, and D. T. HosseinRokni, “Exact free vibration study of rectangular Mindlin plates with all-over part-through open cracks,” Computers and Structures, vol. 88, no. 17-18, pp. 1015–1032, 2010. View at Publisher · View at Google Scholar
  7. Y. Fu, Y. Xiao, and X. Zha, “Nonlinear vibration for moderate thickness rectangular cracked plates including coupled effect of elastic foundation,” Applied Mathematics and Mechanics, vol. 8, no. 26, pp. 963–972, 2005. View at Google Scholar
  8. A. Israr and L. Atepor, “Investigation of the nonlinear dynamics of a partially cracked plate,” in Proceedings of the 7th International Conference on Modern Practice in Stress and Vibration Analysis, vol. 181, 2009. View at Publisher · View at Google Scholar
  9. J. Yang, Y. X. Hao, W. Zhang, and S. Kitipornchai, “Nonlinear dynamic response of a functionally graded plate with a through-width surface crack,” Nonlinear Dynamics, vol. 59, no. 1-2, pp. 207–219, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. A. Saito, M. P. Castanier, and C. Pierre, “Estimation and veering analysis of nonlinear resonant frequencies of cracked plates,” Journal of Sound and Vibration, vol. 326, no. 3–5, pp. 725–739, 2009. View at Publisher · View at Google Scholar · View at Scopus
  11. R. Ismail and M. P. Cartmell, “An investigation into the vibration analysis of a plate with a surface crack of variable angular orientation,” Journal of Sound and Vibration, vol. 331, no. 12, pp. 2929–2948, 2012. View at Publisher · View at Google Scholar · View at Scopus
  12. T. Bose and A. R. Mohanty, “Vibration analysis of a rectangular thin isotropic plate with a part-through surface crack of arbitrary orientation and position,” Journal of Sound and Vibration, vol. 332, no. 26, pp. 7123–7141, 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. H. AsadiGorgi, M. Dardel, and M. H. Pashaei, “Effects of all-over part-through cracks on the aeroelastic characteristics of rectangular panels,” Applied Mathematical Modelling, vol. 39, no. 23-24, pp. 7513–7536, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. M.-H. H. Shen and Y. C. Chu, “Vibrations of beams with a fatigue crack,” Computers and Structures, vol. 45, no. 1, pp. 79–93, 1992. View at Publisher · View at Google Scholar · View at Scopus
  15. N. Pugno, C. Surace, and R. Ruotolo, “Evaluation of the non-linear dynamic response to harmonic excitation of a beam with several breathing cracks,” Journal of Sound and Vibration, vol. 235, no. 5, pp. 749–762, 2000. View at Publisher · View at Google Scholar · View at Scopus
  16. S. Caddemi, I. Caliò, and M. Marletta, “The non-linear dynamic response of the Euler-Bernoulli beam with an arbitrary number of switching cracks,” International Journal of Non-Linear Mechanics, vol. 45, no. 7, pp. 714–726, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. F. E. Dotti, V. H. Cortinez, and F. Reguera, “Non-linear dynamic response to simple harmonic excitation of a thin-walled beam with a breathing crack,” Applied Mathematical Modelling, vol. 40, no. 1, pp. 451–467, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  18. J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, Fla, USA, 2nd edition, 2004.
  19. G. Z. Harris, “The buckling and post-buckling behaviour of composite plates under biaxial loading,” International Journal of Mechanical Sciences, vol. 17, no. 3, pp. 187–202, 1975. View at Publisher · View at Google Scholar · View at Scopus