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Analysis of the Periodic Damping Coefficient Equation Based on Floquet Theory

[+] Author Affiliations
Fatemeh Afzali, Brian F. Feeny

Michigan State University, East Lansing, MI

Gizem D. Acar

University of Maryland, College Park, MD

Paper No. DETC2017-68450, pp. V008T12A050; 7 pages
doi:10.1115/DETC2017-68450
From:
  • ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 8: 29th Conference on Mechanical Vibration and Noise
  • Cleveland, Ohio, USA, August 6–9, 2017
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5822-6
  • Copyright © 2017 by ASME

abstract

In this paper, we study the response of a linear differential equation, for which the damping coefficient varies periodically in time. We use Floquet theory combined with the harmonic balance method to find the approximate solution and capture the stability criteria. Based on Floquet theory the approximate solution includes the exponential part having an unknown exponent, and a periodic part, which is expressed using a truncated series of harmonics. After substituting the assumed response in the equation, the harmonic balance method is applied. We use the characteristic equation of the truncated harmonic series to obtain the Floquet exponents. The free response and stability characteristics of the damped system for a set of parameters are shown.

Copyright © 2017 by ASME
Topics: Damping

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