This brief note studies small transverse vibrations of a long hanging chain of discrete links. Analytical approximate solutions are obtained when the number of links is considered large while they still posses nontrivial rotary inertia. The results imply that the rotary inertia becomes more significant for higher modes of vibration.
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Brief Notes
1.
Watson, G. N., 1966, Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, UK, pp. 3–5.
2.
Routh, E. J., 1955, The Advanced Part of a Treatise on the Dynamics of a System of Rigid Bodies, 6th ed., Dover, New York, pp. 403–405.
3.
Spiegel, M. R., 1981, Applied Differential Equations, 3rd ed., Prentice-Hall, Englewood Cliffs, NJ, pp. 641–645.
4.
Wang
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.5.
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6.
McCreech
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.7.
Levinson
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.8.
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.10.
Weng
, P.-C.
, and Lee
, W.
, 1994
, “Transverse Vibrations of a Hanging Cable: The Limiting Case of a Hanging Chain
,” J. Sound Vib.
, 171
, pp. 574
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.Copyright © 2003
by ASME
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