Parametric excitation of a detuned spherical pendulum

J. W. Miles, Q. P. Zou

Research output: Contribution to journalArticle

Abstract

The weakly non-linear response of a slightly detuned spherical pendulum with natural frequencies ω1 and ω2, ω1 ≈ ω2, subject to parametric excitation at frequency 2ω, is analyzed in the parametric domain ω2 - 1/2; (ω2 1 + ω2 2) = O (εω2), where ε is a measure of the excitation. There is a finite neighbourhood of ω2 = ω2 2, bounded by Hopf-bifurcation points, in which no stable harmonic motion is possible and the motion is either a periodically modulated sinusoid (limit cycle) or chaotic, depending on the frequency offset and dissipation. The analytical predictions are supported by numerical integration, which also reveals that the parametric domains of limit cycles and chaotic motions overlap those of stable harmonic motion. The system provides a model of mode competition in a system with a discrete, infinite spectrum, e.g., Faraday waves.

Original languageEnglish
Pages (from-to)237-250
Number of pages14
JournalJournal of Sound and Vibration
Volume164
Issue number2
DOIs
Publication statusPublished - 22 Jun 1993

ASJC Scopus subject areas

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

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