Non-linear transverse vibrations and 3:1 internal resonances of a tensioned beam on multiple supports

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dc.contributor.authorBaǧdatli S.M.
dc.contributor.authorÖz H.R.
dc.contributor.authorÖzkaya E.
dc.date.accessioned2024-07-22T08:20:20Z
dc.date.available2024-07-22T08:20:20Z
dc.date.issued2011
dc.description.abstractIn this study, nonlinear transverse vibrations of a tensioned Euler-Bernoulli beam resting on multiple supports are investigated. The immovable end conditions due to simple supports cause stretching of neutral axis and introduce cubic nonlinearity to the equations of motion. Forcing and damping effects are included in the analysis. The general arbitrary number of support case is investigated and 3, 4, and 5 support cases analyzed in detail. A perturbation technique (the method of multiple scales) is applied to the equations of motion to obtain approximate analytical solutions. 3:1 internal resonance case is also considered. Natural frequencies and mode shapes for the linear problem are found for the tensioned beam. Nonlinear frequencies are calculated; amplitude and phase modulation figures are presented for different forcing and damping cases. Frequency-response and force-response curves are drawn. Different internal resonance cases between modes are investigated. © Association for Scientific Research.
dc.identifier.issn1300686X
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/18101
dc.language.isoEnglish
dc.subjectControl nonlinearities
dc.subjectDamping
dc.subjectEquations of motion
dc.subjectFrequency response
dc.subjectPhase modulation
dc.subjectResonance
dc.subjectStructural panels
dc.subjectAmplitude and phase modulations
dc.subjectApproximate analytical solutions
dc.subjectArbitrary number
dc.subjectAxial tensions
dc.subjectCubic nonlinearities
dc.subjectDamping effect
dc.subjectEnd conditions
dc.subjectEuler Bernoulli beams
dc.subjectInternal resonance
dc.subjectLinear problems
dc.subjectMethod of multiple scale
dc.subjectMode shapes
dc.subjectNeutral axis
dc.subjectNon-linear
dc.subjectNonlinear frequency
dc.subjectNonlinear transverse vibration
dc.subjectPerturbation method
dc.subjectResponse curves
dc.subjectSimple support
dc.subjectSupported beams
dc.subjectTensioned beam
dc.subjectVibration
dc.subjectPerturbation techniques
dc.titleNon-linear transverse vibrations and 3:1 internal resonances of a tensioned beam on multiple supports
dc.typeArticle

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