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.
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References
Blevins. R. D., 1979,Formulas for Natural Frequency and Mode Shape, Van Nostrand Rein-hold, New York, pp. 240–240.
Boyd, J. P., 1989,Chebyshev and Fourier spectral methods, Lecture notes in engineering 49, Springer-Verlag, Berlin, pp. 213–235.
Deresiewicz, H., 1956, “Symmetric Flexural Vibrations of a Clamped Disk,”Journal of Applied Mechanics, Vol. 12, pp. 319–319.
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.
Fornberg, B., 1996,A Practical Guide to Pseu-dospectral Methods, Cambridge University Press, pp. 87–88 and pp. 110–111.
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.
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.
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.
Irie, T., Yamada, G. and Takagi, K., 1982, “Natural Frequencies of Thick Annular Plates,”Journal of Applied Mechanics, Vol. 49, pp. 633–638.
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)
Lee, J., 2003, “Eigenvalue Analysis of Rectangular Mindlin Plates by Chebyshev Pseu-dospectral Method,”KSME International Journal, Vol. 17, No. 3, pp. 370–379.
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.
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.
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.
Pyret, R. and Taylor, T. D., 1990,Computational methods for fluid flow. Springer-Verlag, pp. 227–247.
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.
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Lee, J. Application of the chebyshev-fourier pseudospectral method to the eigenvalue analysis of circular mindlin plates with free boundary conditions. KSME International Journal 17, 1458–1465 (2003). https://doi.org/10.1007/BF02982325
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DOI: https://doi.org/10.1007/BF02982325