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    Analytical Treatment of In-Plane Parametrically Excited Undamped Vibrations of Simply Supported Parabolic Arches

    Source: Journal of Vibration and Acoustics:;2003:;volume( 125 ):;issue: 001::page 73
    Author:
    Dimitris S. Sophianopoulos
    ,
    Research Fellow
    ,
    George T. Michaltsos
    DOI: 10.1115/1.1521952
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: The present work offers a simple and efficient analytical treatment of the in-plane undamped vibrations of simply supported parabolic arches under parametric excitation. After thoroughly dealing with the free vibration characteristics of the structure dealt with, the differential equations of the forced motion caused by a time dependent axial loading of the form P=P0+Pt cos θt are reduced to a set of Mathieu-Hill type equations. These may be thereafter tackled and the dynamic stability problem comprehensively discussed. An illustrative example based on Bolotin’s approach produces results validating the proposed method.
    keyword(s): Vibration , Arches , Equations , Free vibrations , Differential equations , Dynamic stability AND Motion ,
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      Analytical Treatment of In-Plane Parametrically Excited Undamped Vibrations of Simply Supported Parabolic Arches

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    https://yetl.yabesh.ir/yetl1/handle/yetl/129380
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    • Journal of Vibration and Acoustics

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    contributor authorDimitris S. Sophianopoulos
    contributor authorResearch Fellow
    contributor authorGeorge T. Michaltsos
    date accessioned2017-05-09T00:11:54Z
    date available2017-05-09T00:11:54Z
    date copyrightJanuary, 2003
    date issued2003
    identifier issn1048-9002
    identifier otherJVACEK-28864#73_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/129380
    description abstractThe present work offers a simple and efficient analytical treatment of the in-plane undamped vibrations of simply supported parabolic arches under parametric excitation. After thoroughly dealing with the free vibration characteristics of the structure dealt with, the differential equations of the forced motion caused by a time dependent axial loading of the form P=P0+Pt cos θt are reduced to a set of Mathieu-Hill type equations. These may be thereafter tackled and the dynamic stability problem comprehensively discussed. An illustrative example based on Bolotin’s approach produces results validating the proposed method.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleAnalytical Treatment of In-Plane Parametrically Excited Undamped Vibrations of Simply Supported Parabolic Arches
    typeJournal Paper
    journal volume125
    journal issue1
    journal titleJournal of Vibration and Acoustics
    identifier doi10.1115/1.1521952
    journal fristpage73
    journal lastpage79
    identifier eissn1528-8927
    keywordsVibration
    keywordsArches
    keywordsEquations
    keywordsFree vibrations
    keywordsDifferential equations
    keywordsDynamic stability AND Motion
    treeJournal of Vibration and Acoustics:;2003:;volume( 125 ):;issue: 001
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
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