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KSME International Journal

, 17:1458 | Cite as

Application of the chebyshev-fourier pseudospectral method to the eigenvalue analysis of circular mindlin plates with free boundary conditions

  • Jinhee Lee
Article

Abstract

An eigenvalue analysis of the circular Mindlin plates with free boundary conditions is presented. The analysis is based on the Chebyshev-Fourier pseudospectral method. Even though the eigenvalues of lower vibration modes tend to convergence more slowly than those of higher vibration modes, the eigenvalues converge for sufficiently fine pseudospectral grid resolutions. The eigenvalues of the axisymmetric modes are computed separately. Numerical results are provided for different grid resolutions and for different thickness-to-radius ratios.

Key Words

Eigenvalue Chebyshev-Fourier Pseudospectral Method Circular Mindlin Plate 

References

  1. Blevins. R. D., 1979,Formulas for Natural Frequency and Mode Shape, Van Nostrand Rein-hold, New York, pp. 240–240.Google Scholar
  2. Boyd, J. P., 1989,Chebyshev and Fourier spectral methods, Lecture notes in engineering 49, Springer-Verlag, Berlin, pp. 213–235.Google Scholar
  3. Deresiewicz, H., 1956, “Symmetric Flexural Vibrations of a Clamped Disk,”Journal of Applied Mechanics, Vol. 12, pp. 319–319.Google Scholar
  4. Deresiewicz, H. and Mindlin, R. D., 1955, “Axially Symmetric Flexural Vibration of a Circular Disk,”Transactions of ASME Journal of Applied Mechanics, Vol. 22, pp. 86–88.MATHMathSciNetGoogle Scholar
  5. Fornberg, B., 1996,A Practical Guide to Pseu-dospectral Methods, Cambridge University Press, pp. 87–88 and pp. 110–111.Google Scholar
  6. Gupta, U. S. and Lai, R., 1985, “Axisymmetric Vibrations of Polar Orthotropic Mindlin Annular Plates of Variable Thickness,”Journal of Sound and Vibration, Vol. 98, No. 4, pp. 565–573.CrossRefGoogle Scholar
  7. Irie. T., Yamada, G. and Aomura, S., 1979, “Free Vibration of a Mindlin Annular Plate of Varying Thickness,”Journal of Sound and Vibration, Vol. 66, No. 2, pp. 187–197.CrossRefGoogle Scholar
  8. Irie, T., Yamada, G. and Aomura, S., 1980, “Natural Modes and Natural Frequencies of Mindlin Circular Plates,”Journal of Applied Mechanics, Vol. 47, pp. 652–655.MATHGoogle Scholar
  9. Irie, T., Yamada, G. and Takagi, K., 1982, “Natural Frequencies of Thick Annular Plates,”Journal of Applied Mechanics, Vol. 49, pp. 633–638.CrossRefGoogle Scholar
  10. Lee, J., 2002, “Eigenvalue Analysis of Circular Mindlin Plates Using the Pseudospectral Method,”Transactions of KSME A, Vol. 26, No. 6, pp. 1169–1177. (in Korean with English Abstract)Google Scholar
  11. Lee, J., 2003, “Eigenvalue Analysis of Rectangular Mindlin Plates by Chebyshev Pseu-dospectral Method,”KSME International Journal, Vol. 17, No. 3, pp. 370–379.Google Scholar
  12. Liew. K. M., Han, J. B. and Xiao, Z. M., 1997, “Vibration Analysis of Circular Mindlin Plates Using Differential Quadrature Method,”Journal of Sound and Vibration, Vol. 205, No. 5, pp. 617–630.CrossRefGoogle Scholar
  13. Mikami, T. and Yoshimura, J., 1984, “Application of the Collocation Method to Vibration Analysis of Rectangular Mindlin Plates,”Computers & Structures, Vol. 18, No. 3, pp. 425–432.MATHCrossRefGoogle Scholar
  14. Mindlin, R. D., 1951, “Influence of Rotary Inertia and Shear on Flexural Motion of Isotropie, Elastic Plates,”Transactions of ASME Journal of Applied Mechanics, Vol. 18, pp. 31–38.MATHGoogle Scholar
  15. Pyret, R. and Taylor, T. D., 1990,Computational methods for fluid flow. Springer-Verlag, pp. 227–247.Google Scholar
  16. Soni, S. R. and Amba-Rao, C. L., 1975, “On Radially Symmetric Vibrations of Orthotropic Non-uniform Disks Including Shear Deformation,”Journal of Sound and Vibration, Vol. 42, No. 1, pp. 57–63.MATHCrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2003

Authors and Affiliations

  1. 1.Depertment of Mechano-InformaticsHongik UniversityChoongnamKorea

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