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Journal of Vibration and Acoustics | Volume 122 | Issue 2 | TECHNICAL PAPERS
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
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Copyright © 2000 by ASME
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References

1
Endo,  M., 1972, “Flexural Vibrations of a Ring with Arbitrary Cross Section,” Bull. JSME, 15, pp. 446–454.
2
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.
3
Leissa,  A. W., and So,  J., 1995, “Three-Dimensional Vibration of Truncated Hollow Cones,” J. Vibr. Control, 1, pp. 145–158.
4
Tsui, Edward, Y. W., 1968, Stresses in Shells of Revolution, Pacific Coast Publishers.
5
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.
6
Kantorovich, L. V., and Krylov, V. I., 1958, Approximate Methods in Higher Analysis, Noordhoff, Groningen.
7
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.
8
Abramowitz, M., and Stegun, I. A., 1964, Handbook of Mathematical Functions, U.S. Government Printing Office, Washington, DC.
9
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.
10
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)
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Cross-sections of circular rings with hm/L=1 and Rit/L=3
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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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