Transient tumbling chaos and damping identification for parametric pendulum

Bryan Horton, Marian Wiercigroch, Xu Xu

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

The aim of this study is to provide a simple, yet effective and generally applicable technique for determining damping for parametric pendula. The proposed model is more representative of system dynamics because the numerical results describe the qualitative features of experimentally exhibited transient tumbling chaotic motions well. The assumption made is that the system is accurately modelled by a combination of viscous and Coulomb dampings; a parameter identification procedure is developed from this basis. The results of numerical and experimental time histories of free oscillations are compared with the model produced from the parameters identified by the classic logarithmic decrement technique. The merits of the present method are discussed before the model is verified against experimental results. Finally, emphasis is placed on a close corroboration between the experimental and theoretical transient tumbling chaotic trajectories.

Original languageEnglish
Pages (from-to)767-784
Number of pages18
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences
Volume366
Issue number1866
Early online date18 Oct 2007
DOIs
Publication statusPublished - Mar 2008

Keywords

  • dry friction
  • linear viscosity
  • parameter identification
  • transient tumbling chaos
  • parametric pendula
  • excited pendulum
  • friction
  • oscillators
  • coulomb
  • behavior
  • system

Cite this

@article{d64ae40917324a8d9e7b76b670e74cdb,
title = "Transient tumbling chaos and damping identification for parametric pendulum",
abstract = "The aim of this study is to provide a simple, yet effective and generally applicable technique for determining damping for parametric pendula. The proposed model is more representative of system dynamics because the numerical results describe the qualitative features of experimentally exhibited transient tumbling chaotic motions well. The assumption made is that the system is accurately modelled by a combination of viscous and Coulomb dampings; a parameter identification procedure is developed from this basis. The results of numerical and experimental time histories of free oscillations are compared with the model produced from the parameters identified by the classic logarithmic decrement technique. The merits of the present method are discussed before the model is verified against experimental results. Finally, emphasis is placed on a close corroboration between the experimental and theoretical transient tumbling chaotic trajectories.",
keywords = "dry friction, linear viscosity, parameter identification, transient tumbling chaos, parametric pendula, excited pendulum, friction, oscillators, coulomb, behavior, system",
author = "Bryan Horton and Marian Wiercigroch and Xu Xu",
year = "2008",
month = "3",
doi = "10.1098/rsta.2007.2126",
language = "English",
volume = "366",
pages = "767--784",
journal = "Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences",
issn = "1364-503X",
publisher = "Royal Society Publishing",
number = "1866",

}

TY - JOUR

T1 - Transient tumbling chaos and damping identification for parametric pendulum

AU - Horton, Bryan

AU - Wiercigroch, Marian

AU - Xu, Xu

PY - 2008/3

Y1 - 2008/3

N2 - The aim of this study is to provide a simple, yet effective and generally applicable technique for determining damping for parametric pendula. The proposed model is more representative of system dynamics because the numerical results describe the qualitative features of experimentally exhibited transient tumbling chaotic motions well. The assumption made is that the system is accurately modelled by a combination of viscous and Coulomb dampings; a parameter identification procedure is developed from this basis. The results of numerical and experimental time histories of free oscillations are compared with the model produced from the parameters identified by the classic logarithmic decrement technique. The merits of the present method are discussed before the model is verified against experimental results. Finally, emphasis is placed on a close corroboration between the experimental and theoretical transient tumbling chaotic trajectories.

AB - The aim of this study is to provide a simple, yet effective and generally applicable technique for determining damping for parametric pendula. The proposed model is more representative of system dynamics because the numerical results describe the qualitative features of experimentally exhibited transient tumbling chaotic motions well. The assumption made is that the system is accurately modelled by a combination of viscous and Coulomb dampings; a parameter identification procedure is developed from this basis. The results of numerical and experimental time histories of free oscillations are compared with the model produced from the parameters identified by the classic logarithmic decrement technique. The merits of the present method are discussed before the model is verified against experimental results. Finally, emphasis is placed on a close corroboration between the experimental and theoretical transient tumbling chaotic trajectories.

KW - dry friction

KW - linear viscosity

KW - parameter identification

KW - transient tumbling chaos

KW - parametric pendula

KW - excited pendulum

KW - friction

KW - oscillators

KW - coulomb

KW - behavior

KW - system

U2 - 10.1098/rsta.2007.2126

DO - 10.1098/rsta.2007.2126

M3 - Article

VL - 366

SP - 767

EP - 784

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences

SN - 1364-503X

IS - 1866

ER -