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    Forced Vibrations of Supercritically Transporting Viscoelastic Beams

    Source: Journal of Vibration and Acoustics:;2012:;volume( 134 ):;issue: 005::page 51007
    Author:
    Hu Ding
    ,
    Li-Qun Chen
    ,
    Shao-Pu Yang
    ,
    Guo-Ce Zhang
    DOI: 10.1115/1.4006184
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: This study focuses on the steady-state periodic response of supercritically transporting viscoelastic beams. In the supercritical speed range, forced vibrations are investigated for traveling beams via the multiscale analysis with a numerical confirmation. The forced vibration is excited by the spatially uniform and temporally harmonic vibration of the supporting foundation. A nonlinear integro-partial-differential equation is used to determine steady responses. The straight equilibrium configuration bifurcates in multiple equilibrium positions at supercritical translating speeds. The equation is cast in the standard form of continuous gyroscopic systems via introducing a coordinate transform for nontrivial equilibrium configuration. The natural frequencies and modes of the supercritically traveling beams are analyzed via the Galerkin method for the linear standard form with space-dependent coefficients under the simply supported boundary conditions. Based on the natural frequencies and modes, the method of multiple scales is applied to the governing equation to determine steady-state responses. To confirm results via the method of multiple scales, a finite difference scheme is developed to calculate steady-state response numerically. Quantitative comparisons demonstrate that the approximate analytical results have rather high precision. Numerical results are also presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
    keyword(s): Resonance , Vibration , Equations , Frequency , Galerkin method , Steady state , Travel , Boundary-value problems , Functions AND Equilibrium (Physics) ,
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      Forced Vibrations of Supercritically Transporting Viscoelastic Beams

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    contributor authorHu Ding
    contributor authorLi-Qun Chen
    contributor authorShao-Pu Yang
    contributor authorGuo-Ce Zhang
    date accessioned2017-05-09T00:55:31Z
    date available2017-05-09T00:55:31Z
    date copyrightOctober, 2012
    date issued2012
    identifier issn1048-9002
    identifier otherJVACEK-926081#051007_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/150607
    description abstractThis study focuses on the steady-state periodic response of supercritically transporting viscoelastic beams. In the supercritical speed range, forced vibrations are investigated for traveling beams via the multiscale analysis with a numerical confirmation. The forced vibration is excited by the spatially uniform and temporally harmonic vibration of the supporting foundation. A nonlinear integro-partial-differential equation is used to determine steady responses. The straight equilibrium configuration bifurcates in multiple equilibrium positions at supercritical translating speeds. The equation is cast in the standard form of continuous gyroscopic systems via introducing a coordinate transform for nontrivial equilibrium configuration. The natural frequencies and modes of the supercritically traveling beams are analyzed via the Galerkin method for the linear standard form with space-dependent coefficients under the simply supported boundary conditions. Based on the natural frequencies and modes, the method of multiple scales is applied to the governing equation to determine steady-state responses. To confirm results via the method of multiple scales, a finite difference scheme is developed to calculate steady-state response numerically. Quantitative comparisons demonstrate that the approximate analytical results have rather high precision. Numerical results are also presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleForced Vibrations of Supercritically Transporting Viscoelastic Beams
    typeJournal Paper
    journal volume134
    journal issue5
    journal titleJournal of Vibration and Acoustics
    identifier doi10.1115/1.4006184
    journal fristpage51007
    identifier eissn1528-8927
    keywordsResonance
    keywordsVibration
    keywordsEquations
    keywordsFrequency
    keywordsGalerkin method
    keywordsSteady state
    keywordsTravel
    keywordsBoundary-value problems
    keywordsFunctions AND Equilibrium (Physics)
    treeJournal of Vibration and Acoustics:;2012:;volume( 134 ):;issue: 005
    contenttypeFulltext
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