A non-linear eigenvalue problem associated with inextensible whirling strings

Coomer J., Lazarus M., Tucker R., Kershaw D., Tegman A.

JOURNAL OF SOUND AND VIBRATION, vol.239, no.5, pp.969-982, 2001 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 239 Issue: 5
  • Publication Date: 2001
  • Doi Number: 10.1006/jsvi.2000.3190
  • Journal Name: JOURNAL OF SOUND AND VIBRATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.969-982
  • Ankara University Affiliated: No

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. (C) 2001 Academic Press.