Transition Curve Analysis of Linear Fractional Periodic Time-Delayed Systems Via Explicit Harmonic Balance Method

Eric Butcher, Arman Dabiri, Morad Nazari

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19 Scopus citations

Abstract

This paper presents a technique to obtain the transition curves of fractional periodic time-delayed (FPTD) systems based on a proposed explicit harmonic balance (EHB) method. This method gives the analytical Hill matrix of FPTD systems explicitly with a symbolic computation-free algorithm. Furthermore, all linear operations on Fourier basis vectors including fractional order derivative operators and time-delayed operators for a linear FPTD system are obtained. This technique is illustrated with parametrically excited simple and double pendulum systems, with both time-delayed states and fractional damping.

Original languageEnglish (US)
Article number041005
JournalJournal of Computational and Nonlinear Dynamics
Volume11
Issue number4
DOIs
Publication statusPublished - Jul 1 2016

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ASJC Scopus subject areas

  • Mechanical Engineering
  • Applied Mathematics
  • Control and Systems Engineering

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