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Slow Passage Through Resonance in Mathieu’s Equation

[+] Author Affiliations
Leslie Ng, Richard Rand, Michael O’Neil

Cornell University, Ithaca, NY

Paper No. IMECE2002-39139, pp. 131-140; 10 pages
doi:10.1115/IMECE2002-39139
From:
  • ASME 2002 International Mechanical Engineering Congress and Exposition
  • Design Engineering
  • New Orleans, Louisiana, USA, November 17–22, 2002
  • Conference Sponsors: Design Engineering Division
  • ISBN: 0-7918-3628-2 | eISBN: 0-7918-1691-5, 0-7918-1692-3, 0-7918-1693-1
  • Copyright © 2002 by ASME

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.

Copyright © 2002 by ASME
Topics: Resonance , Equations

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