Nonlinear transverse vibrations and 3:1 internal resonances of a beam with multiple supports

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dc.contributor.authorÖzkaya E.
dc.contributor.authorBaǧdatli S.M.
dc.contributor.authorÖz H.R.
dc.date.accessioned2024-07-22T08:22:32Z
dc.date.available2024-07-22T08:22:32Z
dc.date.issued2008
dc.description.abstractIn this study, nonlinear transverse vibrations of an Euler-Bernoulli beam with multiple supports are considered. The beam is supported with immovable ends. The immovable end conditions cause stretching of neutral axis and introduce cubic nonlinear terms to the equations of motion. Forcing and damping effects are included in the problem. The general arbitrary number of support case is considered at first, and then 3-, 4-, and 5-support cases are investigated The method of multiple scales is directly applied to the partial differential equations. Natural frequencies and mode shapes for the linear problem are found. The correction terms are obtained from the last order of expansion. Nonlinear frequencies are calculated and then amplitude and phase modulation figures are presented for different forcing and damping cases. The 3:1 internal resonances are investigated. External excitation frequency is applied to the first mode and responses are calculated for the first or second mode. Frequency-response and force-response curves are drawn. Copyright © 2008 by ASME.
dc.identifier.DOI-ID10.1115/1.2775508
dc.identifier.issn10489002
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/19122
dc.language.isoEnglish
dc.publisherAmerican Society of Mechanical Engineers(ASME)
dc.subjectDamping
dc.subjectEquations of motion
dc.subjectNonlinear equations
dc.subjectArbitrary number
dc.subjectDamping effect
dc.subjectEnd conditions
dc.subjectEquation of motion
dc.subjectEuler Bernoulli beams
dc.subjectForcings
dc.subjectInternal resonance
dc.subjectNeutral axis
dc.subjectNonlinear terms
dc.subjectNonlinear transverse vibration
dc.subjectFrequency response
dc.titleNonlinear transverse vibrations and 3:1 internal resonances of a beam with multiple supports
dc.typeArticle

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