Slow passage through resonance in mathieu's equation

Leslie Ng, Richard Rand, Michael O'Neil

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

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 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)
Pages131-140
Number of pages10
ISBN (Print)0791836282, 9780791836286
StatePublished - 2002

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Amplification

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

Ng, L., Rand, R., & O'Neil, M. (2002). Slow passage through resonance in mathieu's equation. In Design Engineering (pp. 131-140). American Society of Mechanical Engineers (ASME).

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

Design Engineering. American Society of Mechanical Engineers (ASME), 2002. p. 131-140.

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

Ng, L, Rand, R & O'Neil, M 2002, Slow passage through resonance in mathieu's equation. in Design Engineering. American Society of Mechanical Engineers (ASME), pp. 131-140.
Ng L, Rand R, O'Neil M. Slow passage through resonance in mathieu's equation. In Design Engineering. American Society of Mechanical Engineers (ASME). 2002. p. 131-140
Ng, Leslie ; Rand, Richard ; O'Neil, Michael. / Slow passage through resonance in mathieu's equation. Design Engineering. American Society of Mechanical Engineers (ASME), 2002. pp. 131-140
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