Slow passage through resonance in Mathieu's equation

Leslie Ng, Richard Rand, Michael O'Neil

Research output: Contribution to journalArticlepeer-review


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
Issue number6
StatePublished - Jun 2003


  • Amplification
  • Mathieu equation
  • Parametric excitation
  • Resonance

ASJC Scopus subject areas

  • Automotive Engineering
  • General Materials Science
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering


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