A Non-Linear Eigenvalue Problem Associated with Inextensible Whirling Strings

Author: Coomer J.   Lazarus M.   Tucker R.W.   Kershaw D.   Tegman A.  

Publisher: Academic Press

ISSN: 0022-460X

Source: Journal of Sound and Vibration, Vol.239, Iss.5, 2001-02, pp. : 969-982

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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.