A Floquet-Based Analysis of Parametric Excitation through the Damping Coefficient

Fatemeh Afzali, Gizem D. Acar, Brian F. Feeny

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The Floquet theory has been classically used to study the stability characteristics of linear dynamic systems with periodic coefficients and is commonly applied to Mathieu's equation, which has parametric stiffness. The focus of this article is to study the response characteristics of a linear oscillator for which the damping coefficient varies periodically in time. The Floquet theory is used to determine the effects of mean plus cyclic damping on the Floquet multipliers. An approximate Floquet solution, which includes an exponential part and a periodic part that is represented by a truncated Fourier series, is then applied to the oscillator. Based on the periodic part, the harmonic balance method is used to obtain the Fourier coefficients and Floquet exponents, which are then used to generate the response to the initial conditions, the boundaries of instability, and the characteristics of the free response solution of the system. The coexistence phenomenon, in which the instability wedges disappear and the transition curves overlap, is recovered by this approach, and its features and robustness are examined.

Original languageEnglish
Article number041003
JournalJournal of Vibration and Acoustics, Transactions of the ASME
Volume143
Issue number4
DOIs
StatePublished - Aug 2021

Keywords

  • Coexistence
  • Damped oscillator
  • Damping
  • Floquet theory
  • Harmonic balance
  • Parametric excitation
  • Response characteristics
  • Stability

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