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Eigenvalue Analysis of Rectangular Mindlin Plates by Chebyshev Pseudospectral Method  

Lee, Jinhee (Department of Mechano-Informatics, Hongik University)
Publication Information
Journal of Mechanical Science and Technology / v.17, no.3, 2003 , pp. 370-379 More about this Journal
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
Eigenvalue; Mindlin Plate; Pseudospectral Method; Chebyshev Polynomials;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
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1 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   과학기술학회마을   DOI
2 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
3 Leissa, A. W., 1981, 'Plate Vibration Research (1976-1980): Complicating Effects,' Journal of Sound and Vibration, Vol. 13, No. 10, pp. 19-36   DOI
4 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   DOI   ScienceOn
5 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   DOI   ScienceOn
6 Pyret, R. and Taylor, T. D., 1990, Computational Methods for Fluid Flow, Springer-Verlag, pp. 227-247
7 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   DOI   ScienceOn
8 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   DOI
9 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   DOI   ScienceOn
10 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   DOI   ScienceOn
11 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   DOI   ScienceOn
12 Boyd, J. P., 1989, Chebyshev and Fourier Spectral Methods, Lecture notes in engineering 49, Springer-Verlag, Berlin, pp. 10-11
13 Blevins, R. D., 1979, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold, New York, pp. 258-261
14 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   DOI   ScienceOn
15 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   DOI   ScienceOn
16 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   DOI   ScienceOn