Slow passage through resonance in mathieu's equation

Leslie Ng, Richard Rand, Michael O'Neil

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 travelling through the tongue and the initial conditions. We use the method of multiple scales to obtain a slow flow approximation. The WKB method is then applied to the slow flow equations to get an analytic approximation.

Original languageEnglish (US)
Title of host publicationDesign Engineering
PublisherAmerican Society of Mechanical Engineers (ASME)
Number of pages10
ISBN (Print)0791836282, 9780791836286
StatePublished - 2002

Publication series

NameASME International Mechanical Engineering Congress and Exposition, Proceedings

ASJC Scopus subject areas

  • Mechanical Engineering

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