On the modal equations of large amplitude flexural vibration of beams, plates, rings and shells

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Abstract

In a simple and straight forward manner the modal equations applicable for the large amplitude flexural vibrations of plates and shells are obtained by the Lagrange's method. These equations can easily be specialised to obtain the corresponding equations applicable for beams and rings. The basic nature of the modal equations for beams and plates on the one hand and rings and shells on the other hand are shown to exhibit hard and soft spring characteristics, respectively.

Résumé

On obtient de façon simple et directe, par la méthode de Lagrange, les équations de mode applicables aux vibrations de flexion de grande amplitude de plaques et de coques. On peut facilement particulariser ces équations pour obtenir les équations correspondantes des poutres et des anneaux. On montre que la nature fondamentale des équations de mode pour les poutres et les plaques d'une part et pour les anneaux et les coques d'autre part est de présenter respectivement des caractéristiques de ressort dur et mou.

Zusammenfassung

In einfacher und direkter Weise werden Schwingungsformgleichungen für die Biegeschwingungen grosser Amplitude von Scheiben und Schalen mittels der Lagrange'schen Methode aufgestellt. Diese Gleichungen lassen sich in einfacher Weise umformen, wodurch die entsprechenden Gleichungen für Träger und Ringe erhalten werden. Es wird gezeigt, dass die Gleichungen für Träger und Scheiben bezw. für Ringe und Schalen die Charakteristiken harter bezw, weicher Federn aufweisen.

Реферат

Пo мeтoдy лaгoaнжa, пpocтым и нeпocpeдcтвeнным пyтeм, вывeдeны мoдaльныe ypaвнeния для изгибныч кoлeбaний плacтин и oбoлoчeк в cлyчae кoнeчныч aмплитyд. Пoлyчeнныe зaвиcимocти лeгкo пpeoбpaзyютcя в cooтвeтcтвyющиe ypaвнeния, cпpaвeдливыe для бaлoк и кoлeц.

Ocнoвныe cвoйcтвa мoдaлтныч ypaвнeний для бaлoк и плacтипoк, c oднoй cтopoны, и для кoлeц и oбoлoчeк, c дpyгoй cтopoны, cooтвeтcтвyют чapaктepиcтикaм жecткич и мягкич пpюжин.

References (3)

  • M. Sathyamoorthy et al.

    Non-linear flexural vibrations of certain deformable bodies I

    J. aeronaut. Soc. India

    (1972)
    M. Sathyamoorthy et al.

    Non-linear flexural vibrations of certain deformable bodies II

    J. aeronaut. Soc. India

    (1973)
There are more references available in the full text version of this article.

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