Chaotic non-planar vibrations of the thin elastica. Part I: Experimental observation of planar instability

J. P. Cusumano, F. C. Moon

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Abstract

In this two-part paper, the results of an investigation into the non-linear dynamics of a flexible cantilevered rod (the elastica) with a thin rectangular cross-section are presented. An experimental examination of the dynamics of the elastica over a broad parameter range forms the core of Part I. In Part II, the experimental work is related to a theoretical study of the mechanics of the elastica, and the study of a two-degree-of-freedom model obtained by modal projection. The experimental system used in this investigation is a rod with clamped-free boundary conditions, forced by sinusoidally displacing the clamped end. Planar periodic motions of the driven elastica are shown to lose stability at distinct resonant wedges, and the resulting motions are shown in general to be non-planar, chaotic, bending-torsion oscillations. Non-planar motions in all resonances exhibit energy cascading and dynamic two-well phenomena, and a family of asymmetric, bending-torsion non-linear modes is discovered. Correlation dimension calculations are used to estimate the number of active degrees of freedom in the system.

Original languageEnglish (US)
Pages (from-to)185-208
Number of pages24
JournalJournal of Sound and Vibration
Volume179
Issue number2
DOIs
StatePublished - Jan 12 1995

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering

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