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    Exact Eigensolutions for a Family of Nonuniform Rods With End Point Masses

    Source: Journal of Vibration and Acoustics:;2017:;volume( 139 ):;issue: 005::page 51018
    Author:
    Rubio, Lourdes
    ,
    Fernández-Sáez, José
    ,
    Morassi, Antonino
    DOI: 10.1115/1.4036467
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: In this paper, new exact closed-form solutions for free longitudinal vibration of a one-parameter countable family of cantilever rods with one end tip mass are obtained. The analysis is based on the reduction of the equation governing the longitudinal vibration to the Sturm–Liouville canonical form and on the use of double Darboux transformations. The rods for which exact eigensolutions are provided are explicitly determined in terms of an initial rod with known closed-form eigensolutions. The method can be also extended to include longitudinally vibrating rods with tip mass at both ends.
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      Exact Eigensolutions for a Family of Nonuniform Rods With End Point Masses

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    contributor authorRubio, Lourdes
    contributor authorFernández-Sáez, José
    contributor authorMorassi, Antonino
    date accessioned2017-11-25T07:20:13Z
    date available2017-11-25T07:20:13Z
    date copyright2017/13/7
    date issued2017
    identifier issn1048-9002
    identifier othervib_139_05_051018.pdf
    identifier urihttp://138.201.223.254:8080/yetl1/handle/yetl/4236288
    description abstractIn this paper, new exact closed-form solutions for free longitudinal vibration of a one-parameter countable family of cantilever rods with one end tip mass are obtained. The analysis is based on the reduction of the equation governing the longitudinal vibration to the Sturm–Liouville canonical form and on the use of double Darboux transformations. The rods for which exact eigensolutions are provided are explicitly determined in terms of an initial rod with known closed-form eigensolutions. The method can be also extended to include longitudinally vibrating rods with tip mass at both ends.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleExact Eigensolutions for a Family of Nonuniform Rods With End Point Masses
    typeJournal Paper
    journal volume139
    journal issue5
    journal titleJournal of Vibration and Acoustics
    identifier doi10.1115/1.4036467
    journal fristpage51018
    journal lastpage051018-7
    treeJournal of Vibration and Acoustics:;2017:;volume( 139 ):;issue: 005
    contenttypeFulltext
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