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TECHNICAL PAPERS

Vibration of Thick Circular Disks and Shells of Revolution

[+] Author and Article Information
A. V. Singh, L. Subramaniam

Department of Mechanical and Materials Engineering, The University of Western Ontario, London, ON N6A 5B9, Canada

J. Appl. Mech 70(2), 292-298 (Mar 27, 2003) (7 pages) doi:10.1115/1.1544542 History: Received June 24, 1999; Revised August 29, 2002; Online March 27, 2003
Copyright © 2003 by ASME
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References

McMahon,  G. W., 1964, “Experimental Study of the Vibrations of Solid Isotropic Cylinders,” J. Acoust. Soc. Am., 36, pp. 85–92.
Mirsky,  I., 1964, “Vibrations of Orthotropic, Thick Cylindrical Shells,” J. Acoust. Soc. Am., 36(01), pp. 41–51.
Hutchinson,  J. R., 1972, “Axisymmetric Vibrations of a Free Finite Length Rod,” J. Acoust. Soc. Am., 51, pp. 233–240.
Hutchinson,  J. R., 1980, “Vibrations of Solid Cylinders,” ASME J. Appl. Mech., 47, pp. 901–907.
Hutchinson,  J. R., 1984, “Vibrations of Thick Free Circular Plates, Exact Versus Approximate Solutions,” ASME J. Appl. Mech., 51, pp. 581–585.
Soldatos,  K. P., 1994, “Review of Three Dimensional Dynamic Analyses of Circular Cylinders and Cylindrical Shells,” Appl. Mech. Rev., 47, pp. 501–516.
Leissa,  A. W., and So,  J., 1995, “Comparison of Vibration Frequencies for Rods and Beams From One Dimensional and Three Dimensional Analyses,” J. Acoust. Soc. Am., 98, pp. 2122–2134.
Leissa,  A. W., and So,  J., 1995, “Accurate Vibration Frequencies of Circular Cylinders From Three Dimensional Analysis,” J. Acoust. Soc. Am., 98, pp. 2316–2141.
Young,  P. G., and Dickinson,  S. M., 1994, “Free Vibration of a Class of Solids With Cavities,” Int. J. Mech. Sci., 36(12), pp. 1099–1107.
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Singh,  B., and Saxena,  V., 1995, “Axisymmetric Vibration of a Circular Plate With Double Linear Thickness,” J. Sound Vib., 179, pp. 879–889.
So,  J., and Leissa,  A. W., 1998, “Three Dimensional Vibrations of Thick Circular and Annular Plates,” J. Sound Vib., 209(1), pp. 15–41.
Kalnins,  A., 1964, “Effect of Bending on Vibrations of Spherical Shells,” J. Acoust. Soc. Am., 36(01), pp. 74–81.
Irie,  T., Yamada,  G., and Takagi,  K., 1982, “Natural Frequencies of Thick Annular Plate,” ASME J. Appl. Mech., 49, pp. 633–638.
Singh,  A. V., and Mirza,  S., 1985, “Asymmetric Modes and Associated Eigenvalues for Spherical Shells,” ASME J. Pressure Vessel Technol., 107, pp. 77–82.

Figures

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Cross section of a solid of revolution
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Area to be revolved around z-axis to form a variable thickness circular disk
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Representation of a thick conical shell
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Representation of a thick spherical shell
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Convergence study for a conical shell clamped at the lower open end
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Frequency Ω versus thickness ratio h2/a for a clampedfree tapered disk. Parameters used are b/a=0.0,h1/a=0.50 and ν=0.30.
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Frequency Ω versus thickness ratio h/a for a conical shell free at the top opening and clamped at the bottom. Parameters used are cone angle α=30 deg, L/a=1.0 and ν=0.30.
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Frequency Ω versus thickness ratio h/a for a spherical shell clamped at the open end. Parameters used are ϕ1=0 deg,ϕ2=60 deg, and ν=0.30.

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