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    On the Fundamental Transverse Vibration Frequency of a Free-Free Thin Beam With Identical End Masses

    Source: Journal of Vibration and Acoustics:;2007:;volume( 129 ):;issue: 005::page 656
    Author:
    A. Erturk
    ,
    D. J. Inman
    DOI: 10.1115/1.2776341
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: Current research in vibration-based energy harvesting and in microelectromechanical system technology has focused renewed attention on the vibration of beams with end masses. This paper shows that the commonly accepted and frequently quoted fundamental natural frequency formula for a beam with identical end masses is incorrect. It is also shown that the higher mode frequency expressions suggested in the referred work (, 1958, “ Formulas for the Frequencies Including Higher Frequencies of Uniform Cantilever and Free-Free Beams With Additional Masses at the Ends,” ASME J. Appl. Mech.25, pp. 412) are also incorrect. The correct characteristic (frequency) equation is derived and nondimensional comparisons are made between the results of the previously published formula and the corrected formulation using Euler–Bernoulli beam assumptions. The previous formula is shown to be accurate only for the extreme case of very large end mass to beam mass ratios. Curve fitting is used to report alternative first order and second order polynomial ratio expressions for the first natural frequency, as well as for the frequencies of some higher modes.
    keyword(s): Oscillating frequencies , Vibration , Equations , Formulas , Frequency , Polynomials , Fittings , Errors AND Energy harvesting ,
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      On the Fundamental Transverse Vibration Frequency of a Free-Free Thin Beam With Identical End Masses

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    contributor authorA. Erturk
    contributor authorD. J. Inman
    date accessioned2017-05-09T00:26:20Z
    date available2017-05-09T00:26:20Z
    date copyrightOctober, 2007
    date issued2007
    identifier issn1048-9002
    identifier otherJVACEK-28888#656_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/137105
    description abstractCurrent research in vibration-based energy harvesting and in microelectromechanical system technology has focused renewed attention on the vibration of beams with end masses. This paper shows that the commonly accepted and frequently quoted fundamental natural frequency formula for a beam with identical end masses is incorrect. It is also shown that the higher mode frequency expressions suggested in the referred work (, 1958, “ Formulas for the Frequencies Including Higher Frequencies of Uniform Cantilever and Free-Free Beams With Additional Masses at the Ends,” ASME J. Appl. Mech.25, pp. 412) are also incorrect. The correct characteristic (frequency) equation is derived and nondimensional comparisons are made between the results of the previously published formula and the corrected formulation using Euler–Bernoulli beam assumptions. The previous formula is shown to be accurate only for the extreme case of very large end mass to beam mass ratios. Curve fitting is used to report alternative first order and second order polynomial ratio expressions for the first natural frequency, as well as for the frequencies of some higher modes.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleOn the Fundamental Transverse Vibration Frequency of a Free-Free Thin Beam With Identical End Masses
    typeJournal Paper
    journal volume129
    journal issue5
    journal titleJournal of Vibration and Acoustics
    identifier doi10.1115/1.2776341
    journal fristpage656
    journal lastpage662
    identifier eissn1528-8927
    keywordsOscillating frequencies
    keywordsVibration
    keywordsEquations
    keywordsFormulas
    keywordsFrequency
    keywordsPolynomials
    keywordsFittings
    keywordsErrors AND Energy harvesting
    treeJournal of Vibration and Acoustics:;2007:;volume( 129 ):;issue: 005
    contenttypeFulltext
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