Commenced in January 2007
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Edition: International
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Exact Analysis of Resonance Frequencies of Simply Supported Cylindrical Shells

Authors: A. Farshidianfar, P. Oliazadeh, M. H. Farshidianfar


In order to study the free vibration of simply supported circular cylindrical shells; an analytical procedure is developed and discussed in detail. To identify its’ validity, the exact technique was applied to four different shell theories 1) Soedel, 2) Flugge, 3) Morley-Koiter, and 4) Donnell. The exact procedure was compared favorably with experimental results and those obtained using the numerical finite element method. A literature review reveals that beam functions are used extensively as an approximation for simply supported boundary conditions. The effects of this approximate method were also investigated on the natural frequencies by comparing results with those of the exact analysis.

Keywords: Circular Cylindrical Shell, Free Vibration, Natural Frequency.

Digital Object Identifier (DOI):

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[1] W. Leissa, Vibration of Shells (NASA SP-288), US Government Printing Office, Washington DC, 1973.
[2] M. Amabili, M. P. Paidoussis, "Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid structure interaction,’’ Applied Mechanics Review, vol. 56, pp. 349-381, 2003.
[3] M. Amabili, Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, New York, USA, 2008.
[4] Y. Kurylov, M. Amabili, "Polynomial versus trigonometric expansions for nonlinear vibrations of circular cylindrical shells with different boundary conditions,’’ Journal of Sound and Vibration, vol. 329, pp. 1435-1449, 2010.
[5] A. E. H. Love, On the small free vibrations and deformations of thin shells, Philosophical Transactions of the Royal Society (London) 179A, pp. 491–546, 1888.
[6] W. Flugge, Stresses in Shells, Springer, New York, 1973.
[7] K. K. Livanov, Axisymmeric "vibrations of simply supported cylindrical shells’’, PMM, Vol. 25, pp. 742-745, 1961.
[8] S. A. Rinehart, J. T. S. Wang, "Vibration of simply supported cylindrical shells with longitudinal stiffeners,’’ Journal of Sound and Vibration, vol. 24, pp. 151-163, 1972.
[9] G. B. Warburton, J. Higgs, "Natural frequencies of thin cantilever cylindrical shells,’’ Journal of Sound and Vibration, vol. 11, pp. 335-338, 1970.
[10] C. B. Sharma, "Calculation of natural frequencies of fixed-free circular cylindrical shells,’’ Journal of Sound and Vibration, vol. 35, pp. 55-76, 1974.
[11] J. Callahan, H. Baruh, "A closed-form solution procedure for circular cylindrical shell vibrations,’’ International Journal of Solids and Structures, vol. 36, pp. 2973-3013, 1999.
[12] F. Moussaoui, R. Benamar, R. G. White, "The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic shells, Part I: Coupled transverse-circumferential mode shapes of isotropic circular cylindrical shells of infinite length,’’ Journal of Sound and Vibration, vol. 232, pp. 917-943, 2000.
[13] S. K. Tou, K. K. "Wong, High-precision finite element analysis of cylindrical shells,’’ Journal of Computers and Structures, vol.26, pp. 847-854, 1987.
[14] J. W. Tedesco, C. N. Kostem, A. Kalnins, "Free vibration analysis of circular cylindrical shells,’’ Journal of Computers and Structures, vol. 25, pp. 677-685, 1987.
[15] A. B. Sabir, A. Sfendji, T. G. Hughes, "Strain-based finite element for the natural frequencies of cylindrical shells,’’ Journal of Thin-Walled Structures vol. 18, pp. 67-82, 1994.
[16] X. M. Zhang, G. R. Liu, K. Y. Lam, "Vibration analysis of thin cylindrical shells using wave propagation approach,’’ Journal of Sound and Vibration, vol. 239, pp. 397-403, 2001.
[17] A. Farshidianfar, M. H. Farshidianfar, M. J. Crocker, W. O. Smith, "The vibration analysis of long cylindrical shells using acoustical excitation,’’ Journal of Sound and Vibration, vol. 232, pp. 917-943, 2010.
[18] W. Soedel, Vibrations of Shells and Plates, 3rd ed., Marcel Dekker, Inc., 2004.
[19] J. Callahan, Cylindrical shell vibrations: Closed-form analysis and measurement via piezoelectric films, PHD Dissertation, New Brunswick Rutgers, The State University of New Jersey, October 1997.