Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지

Eigenvalue Analysis of Rectangular Mindlin Plates by Chebyshev Pseudospectral Method

  • Lee, Jinhee (Department of Mechano-Informatics, Hongik University)
  • Published : 2003.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

A study of free vibration of rectangular Mindlin plates is presented. The analysis is based on the Chebyshev pseudospectral method, which uses test functions that satisfy the boundary conditions as basis functions. The result shows that rapid convergence and accuracy as well as the conceptual simplicity are achieved when the pseudospectral method is applied to the solution of eigenvalue problems. Numerical examples of rectangular Mindlin plates with clamped and simply supported boundary conditions are provided for various aspect ratios and thickness-to length ratios.

Keywords

References

  1. Bert, C. W. and Malik, M., 1996, 'Differential Quadrature Method in Computational Mechanics : A Review,' Applied Mechanics Review, Vol. 49, No. 1, pp. 1-28 https://doi.org/10.1115/1.3101882
  2. Blevins, R. D., 1979, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold, New York, pp. 258-261
  3. Boyd, J. P., 1989, Chebyshev and Fourier Spectral Methods, Lecture notes in engineering 49, Springer-Verlag, Berlin, pp. 10-11
  4. Chakraverty, S., Bhat, R. B. and Stiharu, I., 1999, 'Recent Research on Vibration of Structures Using Boundary Characteristic orthogonal Polynomials in Rayleigh-Ritz Method,' The Shock and Vibration Digest, Vol. 31, No. 3, pp. 187-194 https://doi.org/10.1177/058310249903100301
  5. Dawe, D. J. and Roufaeil, O. L., 1980, 'Rayleigh-Ritz Vibration Analysis of Mindlin Plates,' Journal of Sound and Vibration, Vol. 69, pp. 345-359 https://doi.org/10.1016/0022-460X(80)90477-0
  6. Gupta, U. S. and Lal, 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 https://doi.org/10.1016/0022-460X(85)90261-5
  7. Lee, J., 2002, 'Eigenvalue Analysis of Circular Mindlin Plates Using the Pseudospectral Method,' Journal of Korean Society of Mechanical Engineers A (Korean with English abstract), Vol. 26, No. 6, pp. 1169-1177 https://doi.org/10.3795/KSME-A.2002.26.6.1169
  8. Lee, U. S. and Lee, J. K., 1998, 'Vibration Analysis of the Plates Subject to Distributed Dynamic Loads by Using Spectral Element Method,' KSME International Journal, Vol. 12, No. 4, pp. 565-571
  9. Leissa, A. W., 1981, 'Plate Vibration Research (1976-1980): Complicating Effects,' Journal of Sound and Vibration, Vol. 13, No. 10, pp. 19-36 https://doi.org/10.1177/058310248101301004
  10. Leissa, A. W., 1987, 'Recent Studies in Plate Vibration (1981-1985) : part Ⅱ, Complicating Effects,' Journal of Sound and Vibration, Vol. 19, No. 3, pp. 10-24 https://doi.org/10.1177/058310248701900304
  11. Liew, K. M. and Teo, T. M., 1999, 'Three-Dimensional Vibration Analysis of Rectangular Plates Based on Differential Quadrature Method,' Journal of Sound and Vibration, Vol. 220, No. 4, pp. 577-599 https://doi.org/10.1006/jsvi.1998.1927
  12. Liew, K. M., Xiang, Y. and Kitipornchai, S., 1995, 'Research on Thick Plate Vibration: A Litterature Survey,' Journal of Sound and Vibration, Vol. 180, No. 1, pp. 163-176 https://doi.org/10.1006/jsvi.1995.0072
  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 https://doi.org/10.1016/0045-7949(84)90062-2
  14. Pyret, R. and Taylor, T. D., 1990, Computational Methods for Fluid Flow, Springer-Verlag, pp. 227-247
  15. Soni, S. R. and Amba-Rao, C. L., 1975, 'On Radially Sysymmetric Vibrations of Orthotropic Non-Uniform Disks Including Shear Deformation,' Journal of Sound and Vibration, Vol. 42, No. 1, pp. 57-63 https://doi.org/10.1016/0022-460X(75)90302-8
  16. Srinivas, S. and Rao, A. K., 1970, 'Vibration and Buckling of Simply Supported Thick Orthotropic Rectangular Plates and Laminates,' International Journal of Solids and Structures, Vol. 6, pp. 1463-1481 https://doi.org/10.1016/0020-7683(70)90076-4