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A non-linear Eigenvalue problem associated with inextensible whirling strings

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<mark>Journal publication date</mark>1/02/2001
<mark>Journal</mark>Journal of Sound and Vibration
Issue number5
Volume239
Number of pages14
Pages (from-to)969-982
Publication StatusPublished
<mark>Original language</mark>English

Abstract

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.