A non-linear Eigenvalue problem associated with inextensible whirling strings

Coomer, J. and Lazarus, Max and Tucker, Robin and Kershaw, D. and Tegman, A. (2001) A non-linear Eigenvalue problem associated with inextensible whirling strings. Journal of Sound and Vibration, 239 (5). pp. 969-982. ISSN 0022-460X

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The motion of idealized inextensible strings is discussed. The equations of motion are analyzed for closed-loop configurations, free of body forces and open hanging strings whirling under gravity. The latter give rise to an interesting non-linear eigenvalue problem describing a spectrum of whirling modes that is amenable to numerical investigation by using the shooting method for two-point boundary value problems. The spectrum is compared with that for small amplitude excitations in both fixed and rotating vertical plane through the suspension point. The results provide a useful theoretical background for an analysis of a laboratory exploration of whirling chains.

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Journal Article
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Journal of Sound and Vibration
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11 Aug 2015 11:35
Last Modified:
22 Nov 2022 02:07