A general solution procedure for the forced vibrations of a system with cubic nonlinearities: Three-to-one internal resonances with external excitation

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dc.contributor.authorBurak Özhan B.
dc.contributor.authorPakdemirli M.
dc.date.accessioned2024-07-22T08:20:53Z
dc.date.available2024-07-22T08:20:53Z
dc.date.issued2010
dc.description.abstractA general vibrational model of a continuous system with arbitrary linear and cubic operators is considered. Approximate analytical solutions are found using the method of multiple scales. The primary resonances of the external excitation and three-to-one internal resonances between two arbitrary natural frequencies are treated. The amplitude and phase modulation equations are derived. The steady-state solutions and their stability are discussed. The solution algorithm is applied to two specific problems: (1) axially moving Euler-Bernoulli beam, and (2) axially moving viscoelastic beam. © 2010 Elsevier Ltd. All rights reserved.
dc.identifier.DOI-ID10.1016/j.jsv.2010.01.010
dc.identifier.issn10958568
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/18371
dc.language.isoEnglish
dc.subjectResonance
dc.subjectApproximate analytical solutions
dc.subjectContinuous system
dc.subjectCubic nonlinearities
dc.subjectEuler Bernoulli beams
dc.subjectExternal excitation
dc.subjectForced vibration
dc.subjectGeneral solutions
dc.subjectInternal resonance
dc.subjectMethod of multiple scale
dc.subjectPrimary resonance
dc.subjectSolution algorithms
dc.subjectSpecific problems
dc.subjectSteady state solution
dc.subjectVibrational models
dc.subjectViscoelastic beams
dc.subjectMathematical operators
dc.titleA general solution procedure for the forced vibrations of a system with cubic nonlinearities: Three-to-one internal resonances with external excitation
dc.typeArticle

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