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

Eric Butcher, Arman Dabiri, Morad Nazari

Research output: Contribution to journalArticle

19 Citations (Scopus)

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
StatePublished - Jul 1 2016

Fingerprint

Harmonic Balance
Pendulums
Fractional
Damping
Derivatives
Curve
Symbolic Computation
Pendulum
Operator
Fractional Order
Derivative

ASJC Scopus subject areas

  • Mechanical Engineering
  • Applied Mathematics
  • Control and Systems Engineering

Cite this

Transition Curve Analysis of Linear Fractional Periodic Time-Delayed Systems Via Explicit Harmonic Balance Method. / Butcher, Eric; Dabiri, Arman; Nazari, Morad.

In: Journal of Computational and Nonlinear Dynamics, Vol. 11, No. 4, 041005, 01.07.2016.

Research output: Contribution to journalArticle

@article{e7d434e76e9c4d22851b41d36044d2f4,
title = "Transition Curve Analysis of Linear Fractional Periodic Time-Delayed Systems Via Explicit Harmonic Balance Method",
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.",
author = "Eric Butcher and Arman Dabiri and Morad Nazari",
year = "2016",
month = "7",
day = "1",
doi = "10.1115/1.4031840",
language = "English (US)",
volume = "11",
journal = "Journal of Computational and Nonlinear Dynamics",
issn = "1555-1415",
publisher = "American Society of Mechanical Engineers(ASME)",
number = "4",

}

TY - JOUR

T1 - Transition Curve Analysis of Linear Fractional Periodic Time-Delayed Systems Via Explicit Harmonic Balance Method

AU - Butcher, Eric

AU - Dabiri, Arman

AU - Nazari, Morad

PY - 2016/7/1

Y1 - 2016/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84947460667&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947460667&partnerID=8YFLogxK

U2 - 10.1115/1.4031840

DO - 10.1115/1.4031840

M3 - Article

AN - SCOPUS:84947460667

VL - 11

JO - Journal of Computational and Nonlinear Dynamics

JF - Journal of Computational and Nonlinear Dynamics

SN - 1555-1415

IS - 4

M1 - 041005

ER -