A relatively thin—thickness to radius ratio—circular ring with rectangular cross section has been investigated to numerically evaluate the effect of eccentricity on the in plane bending natural frequencies and mode shapes. The assumed boundary conditions correspond to a ring freely supported in space such that it is free to translate and rotate with rigid body motion. A truncated Fourier series solution is assumed in an energy formulation to obtain numerical approximations of the eigenvalues and the corresponding eigenvectors for different eccentricities. Extensional and inextensional models for both Flu¨gge and Love-Timoshenko ring models were considered with two thickness to radius ratios. Results show different rates of decrease in the magnitudes of the natural frequencies for different mode configurations. Existence of closely spaced frequencies along with modal coupling are noticeable at 50 percent eccentricity.
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November 1975
This article was originally published in
Journal of Engineering for Industry
Research Papers
Influence of Geometric Imperfections on Vibrational Frequencies of Thin Rings
Joseph R. Gartner,
Joseph R. Gartner
U-139, Mechanical Engineering Department, University of Connecticut, Storrs, Conn.
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Shrikant T. Bhat
Shrikant T. Bhat
U-139, Mechanical Engineering Department, University of Connecticut, Storrs, Conn.
Search for other works by this author on:
Joseph R. Gartner
U-139, Mechanical Engineering Department, University of Connecticut, Storrs, Conn.
Shrikant T. Bhat
U-139, Mechanical Engineering Department, University of Connecticut, Storrs, Conn.
J. Eng. Ind. Nov 1975, 97(4): 1199-1203
Published Online: November 1, 1975
Article history
Received:
June 4, 1975
Online:
July 15, 2010
Citation
Gartner, J. R., and Bhat, S. T. (November 1, 1975). "Influence of Geometric Imperfections on Vibrational Frequencies of Thin Rings." ASME. J. Eng. Ind. November 1975; 97(4): 1199–1203. https://doi.org/10.1115/1.3438728
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