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Mathematical Problems in Engineering
Volume 2016, Article ID 9475397, 20 pages
http://dx.doi.org/10.1155/2016/9475397
Research Article

Frequency Domain Spectral Element Model for the Vibration Analysis of a Thin Plate with Arbitrary Boundary Conditions

Department of Mechanical Engineering, Inha University, 100 Inha-ro, Nam-gu, Incheon 402-751, Republic of Korea

Received 6 June 2016; Revised 4 August 2016; Accepted 5 September 2016

Academic Editor: Giovanni Garcea

Copyright © 2016 Ilwook Park 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. W. Leissa, “Vibration of plates,” NASA SP-160, US Government Printing Office, Washington, DC, USA, 1969. View at Google Scholar
  2. D. J. Gorman, Free Vibration Analysis of Rectangular Plates, Elsevier, New York, NY, USA, 1982.
  3. J. F. Doyle, Wave Propagation in Structures: An FFT-Based Spectral Analysis Methodology, Springer, New York, NY, USA, 1989.
  4. U. Lee, Spectral Element Method in Structural Dynamics, John Wiley & Sons, Singapore, 2009.
  5. I. Park, U. Lee, and D. Park, “Transverse vibration of the thin plates: frequency-domain spectral element modeling and analysis,” Mathematical Problems in Engineering, vol. 2015, Article ID 541276, 15 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. R. S. Langley, “Application of the dynamic stiffness method to the free and forced vibrations of aircraft panels,” Journal of Sound and Vibration, vol. 135, no. 2, pp. 319–331, 1989. View at Publisher · View at Google Scholar · View at Scopus
  7. A. N. Berçin, “Analysis of orthotropic plate structures by the direct-dynamic stiffness method,” Mechanics Research Communications, vol. 22, no. 5, pp. 461–466, 1995. View at Publisher · View at Google Scholar · View at Scopus
  8. A. Y. T. Leung and W. E. Zhou, “Dynamic stiffness analysis of laminated composite plates,” Thin-Walled Structures, vol. 25, no. 2, pp. 109–133, 1996. View at Publisher · View at Google Scholar · View at Scopus
  9. U. Lee and J. Lee, “Spectral-element method for Levy-type plates subject to dynamic loads,” Journal of Engineering Mechanics, vol. 125, no. 2, pp. 243–247, 1999. View at Publisher · View at Google Scholar · View at Scopus
  10. F. Shirmohammadi, S. Bahrami, M. M. Saadatpour, and A. Esmaeily, “Modeling wave propagation in moderately thick rectangular plates using the spectral element method,” Applied Mathematical Modelling, vol. 39, no. 12, pp. 3481–3495, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. U. Orrenius and S. Finnveden, “Calculation of wave propagation in rib-stiffened plate structures,” Journal of Sound and Vibration, vol. 198, no. 2, pp. 203–224, 1996. View at Publisher · View at Google Scholar · View at Scopus
  12. M. Krawczuk, M. Palacz, and W. Ostachowicz, “Wave propagation in plate structures for crack detection,” Finite Elements in Analysis and Design, vol. 40, no. 9-10, pp. 991–1004, 2004. View at Publisher · View at Google Scholar · View at Scopus
  13. A. Chakraborty and S. Gopalakrishnan, “A spectral finite element model for wave propagation analysis in laminated composite plate,” Journal of Vibration and Acoustics-Transactions of the ASME, vol. 128, no. 4, pp. 477–488, 2006. View at Publisher · View at Google Scholar · View at Scopus
  14. W. M. Ostachowicz, “Damage detection of structures using spectral finite element method,” Computers and Structures, vol. 86, no. 3–5, pp. 454–462, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. E. Barbieri, A. Cammarano, S. De Rosa, and F. Franco, “Waveguides of a composite plate by using the spectral finite element approach,” Journal of Vibration and Control, vol. 15, no. 3, pp. 347–367, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. F. Birgersson, S. Finnveden, and C.-M. Nilsson, “A spectral super element for modelling of plate vibration. Part 1: general theory,” Journal of Sound and Vibration, vol. 287, no. 1-2, pp. 297–314, 2005. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Mitra and S. Gopalakrishnan, “Wave propagation analysis in anisotropic plate using wavelet spectral element approach,” Journal of Applied Mechanics, Transactions ASME, vol. 75, no. 1, Article ID 014504, pp. 1–6, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. J. Park, I. Park, and U. Lee, “Transverse vibration and waves in a membrane: frequency domain spectral element modeling and analysis,” Mathematical Problems in Engineering, vol. 2014, Article ID 642782, 14 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. I. Park and U. Lee, “Spectral element modeling and analysis of the transverse vibration of a laminated composite plate,” Composite Structures, vol. 134, pp. 905–917, 2015. View at Publisher · View at Google Scholar · View at Scopus
  20. W. C. Reynolds, Solution of Partial Differential Equations, Department of Mechanical Engineering, Stanford University, Stanford, Calif, USA, 1981.
  21. ANSYS Release 11.0 Documentation for ANSYS, ANSYS, Inc, Canonsburg, PA, USA, 2006.
  22. T. Y. Yang, Finite Element Structural Analysis, Prentice Hall, Upper Saddle River, NJ, USA, 1986.
  23. MATLAB User's Guide, The MathWorks, Natick, Mass, USA, 1993.
  24. L. Meirovitch, Principles and Techniques of Vibrations, Prentice Hall, Upper Saddle River, NJ, USA, 1997.