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Fractional Mathieu Equation

[+] Author Affiliations
Richard H. Rand, Meghan K. Suchorsky

Cornell University, Ithaca, NY

Si M. Sah

University Hassan II-Aïn Chock, Casablanca, Morocco

Paper No. DETC2010-28068, pp. 873-881; 9 pages
doi:10.1115/DETC2010-28068
From:
  • ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 22nd International Conference on Design Theory and Methodology; Special Conference on Mechanical Vibration and Noise
  • Montreal, Quebec, Canada, August 15–18, 2010
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4413-7 | eISBN: 978-0-7918-3881-5
  • Copyright © 2010 by ASME

abstract

After reviewing the concept of fractional derivative, we derive expressions for the transition curves separating regions of stability from regions of instability in the ODE:

x + (δ + εcost)x + cDαx = 0
where Dα x is the order α derivative of x(t), where 0 < α < 1. We use the method of harmonic balance and obtain both a lowest order approximation as well as a higher order approximation for the n = 1 transition curves. We also obtain an expression for the n = 0 transition curves.

Copyright © 2010 by ASME

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