Slow passage through resonance in Mathieu's equation

Leslie Ng, Richard Rand, Michael O'Neil

Research output: Contribution to journalArticle

Abstract

We investigate slow passage through the 2:1 resonance tongue in Mathieu's equation. Using numerical integration, we find that amplification or de-amplification can occur. The amount of amplification (or de-amplification) depends on the speed of travel through the tongue and the initial conditions. We use the method of multiple scales to obtain a slow flow approximation. The Wentzel-Kramers-Brillouin (WKB) method is then applied to the slow equations to obtain an analytic approximation.

Original languageEnglish (US)
Pages (from-to)685-707
Number of pages23
JournalJVC/Journal of Vibration and Control
Volume9
Issue number6
DOIs
StatePublished - Jun 2003

Fingerprint

Mathieu function
Amplification
tongue
approximation
numerical integration
travel

Keywords

  • Amplification
  • Mathieu equation
  • Parametric excitation
  • Resonance

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Computational Mechanics
  • Acoustics and Ultrasonics

Cite this

Slow passage through resonance in Mathieu's equation. / Ng, Leslie; Rand, Richard; O'Neil, Michael.

In: JVC/Journal of Vibration and Control, Vol. 9, No. 6, 06.2003, p. 685-707.

Research output: Contribution to journalArticle

Ng, Leslie ; Rand, Richard ; O'Neil, Michael. / Slow passage through resonance in Mathieu's equation. In: JVC/Journal of Vibration and Control. 2003 ; Vol. 9, No. 6. pp. 685-707.
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