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TECHNICAL PAPERS

Three-Dimensional Vibrations of Thick, Circular Rings with Isosceles Trapezoidal and Triangular Cross-Sections

[+] Author and Article Information
Jae-Hoon Kang

School of Constructional & Environmental System Engineering, Kyongju University, Kyongju, Kyongbook, South Korea

Arthur W. Leissa

Applied Mechanics Program, The Ohio State University, Columbus, OH 43210

J. Vib. Acoust 122(2), 132-139 (Feb 01, 1999) (8 pages) doi:10.1115/1.568449 History: Received February 01, 1999
Copyright © 2000 by ASME
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References

Endo,  M., 1972, “Flexural Vibrations of a Ring with Arbitrary Cross Section,” Bull. JSME, 15, pp. 446–454.
Singal,  R. K., and Williams,  K., 1988, “A Theoretical and Experimental Study of Vibrations of Thick Circular Cylindrical Shells and Rings,” J. Vibr. Acoust. Stress, Reliability Design, 110, pp. 533–537.
Leissa,  A. W., and So,  J., 1995, “Three-Dimensional Vibration of Truncated Hollow Cones,” J. Vibr. Control, 1, pp. 145–158.
Tsui, Edward, Y. W., 1968, Stresses in Shells of Revolution, Pacific Coast Publishers.
Kang, J. H., 1997, “Three-Dimensional Vibration Analysis of Thick Shells ofRevolution with Arbitrary Curvature and Variable Thickness,” Ph.D. Dissertation, The Ohio State University.
Kantorovich, L. V., and Krylov, V. I., 1958, Approximate Methods in Higher Analysis, Noordhoff, Groningen.
Ritz,  W., 1909, “Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik,” J. für die Reine und Angewandte Mathematik, 135, pp. 1–61.
Abramowitz, M., and Stegun, I. A., 1964, Handbook of Mathematical Functions, U.S. Government Printing Office, Washington, DC.
Leissa,  A. W., and So,  J., 1995, “Comparisons of Vibration Frequencies for rods and beams from One-Dimensional and Three-Dimensional Analyses,” J. Acoust. Soc. Am., 98, No. 4, pp. 2122–2135.
So,  J., and Leissa,  A. W., 1997, “Free Vibrations of Thick Hollow Circular Cylinders from Three-Dimensional Analysis,” ASME J. Vibr. Acoust., 119, pp. 89–95.

Figures

Grahic Jump Location
A circular ring with isosceles trapezoidal cross-section and the coordinate system (s,z,θ)
Grahic Jump Location
Cross-sections of circular rings with hm/L=1 and Rit/L=3
Grahic Jump Location
Cross-sections of circular rings with equilateral triangular cross-section for ht/hb=0,hm/L=1/3, and Rit/L=4/3

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