Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams

Hamed Farokhi, Mergen H. Ghayesh, Shahid Hussain

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The three-dimensional nonlinear global dynamics of an axially moving viscoelastic beam is investigated numerically, retaining longitudinal, transverse, and lateral displacements and inertia. The nonlinear continuous model governing the motion of the system is obtained by means of Hamilton's principle. The Galerkin scheme along with suitable eigenfunctions is employed for model reduction. Direct time-integration is conducted upon the reduced-order model yielding the time-varying generalized coordinates. From the time histories of the generalized coordinates, the bifurcation diagrams of Poincaré sections are constructed by varying either the forcing amplitude or the axial speed as the bifurcation parameter. The results for the three-dimensional viscoelastic model are compared to those of a three-dimensional elastic model in order to better understand the effect of the internal energy dissipation mechanism on the dynamical behavior of the system. The results are also presented by means of time histories, phase-plane diagrams, and fast Fourier transforms (FFT).

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalJournal of Vibration and Acoustics, Transactions of the ASME
Volume138
Issue number1
Early online date26 Oct 2015
DOIs
Publication statusPublished - 1 Feb 2016
Externally publishedYes

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diagrams
histories
retaining
internal energy
Eigenvalues and eigenfunctions
inertia
Fast Fourier transforms
Energy dissipation
eigenvectors
energy dissipation

Cite this

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title = "Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams",
abstract = "The three-dimensional nonlinear global dynamics of an axially moving viscoelastic beam is investigated numerically, retaining longitudinal, transverse, and lateral displacements and inertia. The nonlinear continuous model governing the motion of the system is obtained by means of Hamilton's principle. The Galerkin scheme along with suitable eigenfunctions is employed for model reduction. Direct time-integration is conducted upon the reduced-order model yielding the time-varying generalized coordinates. From the time histories of the generalized coordinates, the bifurcation diagrams of Poincar{\'e} sections are constructed by varying either the forcing amplitude or the axial speed as the bifurcation parameter. The results for the three-dimensional viscoelastic model are compared to those of a three-dimensional elastic model in order to better understand the effect of the internal energy dissipation mechanism on the dynamical behavior of the system. The results are also presented by means of time histories, phase-plane diagrams, and fast Fourier transforms (FFT).",
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Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams. / Farokhi, Hamed; Ghayesh, Mergen H.; Hussain, Shahid.

In: Journal of Vibration and Acoustics, Transactions of the ASME, Vol. 138, No. 1, 01.02.2016, p. 1-11.

Research output: Contribution to journalArticle

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AU - Hussain, Shahid

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N2 - The three-dimensional nonlinear global dynamics of an axially moving viscoelastic beam is investigated numerically, retaining longitudinal, transverse, and lateral displacements and inertia. The nonlinear continuous model governing the motion of the system is obtained by means of Hamilton's principle. The Galerkin scheme along with suitable eigenfunctions is employed for model reduction. Direct time-integration is conducted upon the reduced-order model yielding the time-varying generalized coordinates. From the time histories of the generalized coordinates, the bifurcation diagrams of Poincaré sections are constructed by varying either the forcing amplitude or the axial speed as the bifurcation parameter. The results for the three-dimensional viscoelastic model are compared to those of a three-dimensional elastic model in order to better understand the effect of the internal energy dissipation mechanism on the dynamical behavior of the system. The results are also presented by means of time histories, phase-plane diagrams, and fast Fourier transforms (FFT).

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