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Technical Briefs

Vibration Analysis of Clamped, Complete Conical Shells of Revolution From a Three-Dimensional Theory

[+] Author and Article Information
Jae-Hoon Kang

Professor
Department of Architectural Engineering,
Chung-Ang University,
221 Heuksuk-Dong, Dongjak-Ku,
Seoul 156-756, South Korea
e-mail: jhkang@cau.ac.kr

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 9, 2012; final manuscript received March 22, 2013; accepted manuscript posted May 6, 2013; published online August 22, 2013. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 81(1), 014501 (Aug 22, 2013) (3 pages) Paper No: JAM-12-1187; doi: 10.1115/1.4024401 History: Received May 09, 2012; Revised March 22, 2013; Accepted May 06, 2013

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies of clamped, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. A convergence study is presented. The frequencies from the present 3D analysis are compared with those from other 3D methods and 2D thin shell theory.

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References

Kang, J.-H., and Leissa, A. W., 2004, “Three-Dimensional Vibration Analysis of Thick Complete Conical Shells,” ASME J. Appl. Mech., 71(4), pp. 502–507. [CrossRef]
Kang, J.-H., and Leissa, A. W., 2005, “Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory,” ASME J. Appl. Mech., 72(5), pp. 797–800. [CrossRef]
Zhou, D., Au, F. T. K., Cheung, Y. K., and Lo, S. H., 2003, “Three-Dimensional Vibration Analysis of Circular and Annular Plates Via the Chebyshev-Ritz Method,” Int. J. Solids Struct., 40, pp. 3089–3105. [CrossRef]
Liew, K. M., and Yang, B., 1999, “Three-Dimensional Elasticity Solutions for Free Vibrations of Circular Plates: A Polynomials-Ritz Analysis,” Comput. Methods Appl. Mech. Eng., 175, pp. 189–201. [CrossRef]
Dreher, J. F., 1966, “Axisymmetic Vibration of Thin Conical Shells,” Ph.D. thesis, Ohio State University, Columbus, OH.
Dreher, J. F., and Leissa, A. W., 1968, “Axisymmetric Vibration of Thin Conical Shells,” Proceedings of the 4th Southwestern Conference on Theoretical and Applied Mechanics, New Orleans, LA, February 29–March 1, Pergamon Press, New York, pp. 163–181.

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