Free Vibrations of Thick Hollow Circular Cylinders From Three-Dimensional Analysis

[+] Author and Article Information
Jinyoung So

Integrated Systems Technology Korea, Inc., Seoul, Korea

A. W. Leissa

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

J. Vib. Acoust 119(1), 89-95 (Jan 01, 1997) (7 pages) doi:10.1115/1.2889692 History: Received March 01, 1994; Revised April 01, 1995; Online February 26, 2008


A three-dimensional (3-D) method of analysis is developed for the free vibration frequencies of hollow circular cylinders of elastic material. The method is based upon local coordinates whose origin is attached to the center of cylindrical wall. It assumes for the three displacement components a Fourier series in the circumferential (θ) direction and algebraic polynomials in the radial (q) and axial (z) directions. Convergence studies for completely free cylinders show that the analysis can yield frequencies which are exact to five or six significant figures. These accurate frequencies are compared with those from other 3-D analyses available for free hollow circular cylinders having various length-to-outside diameter (L/Do ) and inside-to-outside diameter (Di /Do ) ratios. Extensive, accurate data are presented for the first 10 frequencies of each circumferential wave number 0 through 5 for hollow circular cylinders having Di /Do of 0.1, 0.5, and 0.9, with L/Do = 0.2, 1 and 5 and a Poisson’s ratio (v) = 0.3.

Copyright © 1997 by The American Society of Mechanical Engineers
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