A general solution procedure for the forced vibrations of a continuous system with cubic nonlinearities: Primary resonance case

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dc.contributor.authorBurak Özhan B.
dc.contributor.authorPakdemirli M.
dc.date.accessioned2024-07-22T08:21:29Z
dc.date.available2024-07-22T08:21:29Z
dc.date.issued2009
dc.description.abstractNonlinear vibrations of a general model of continuous system is considered. The model consists of arbitrary linear and cubic operators. The equation of motion is solved by the method of multiple scales (a perturbation method). The primary resonances of external excitation is analysed. The amplitude and phase modulation equations are presented. Approximate analytical solution is derived. Steady-state solutions and their stability are discussed. Finally, the solution algorithm is applied to two different engineering problems. One of the application is the transverse vibration of an axially moving Euler-Bernoulli beam and the other is a viscoelastic beam. © 2009.
dc.identifier.DOI-ID10.1016/j.jsv.2009.04.009
dc.identifier.issn10958568
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/18643
dc.language.isoEnglish
dc.subjectCircuit resonance
dc.subjectControl nonlinearities
dc.subjectMathematical operators
dc.subjectPerturbation techniques
dc.subjectApproximate analytical solutions
dc.subjectContinuous system
dc.subjectCubic nonlinearities
dc.subjectEngineering problems
dc.subjectEquation of motion
dc.subjectEuler Bernoulli beams
dc.subjectExternal excitation
dc.subjectForced vibration
dc.subjectGeneral model
dc.subjectGeneral solutions
dc.subjectMethod of multiple scale
dc.subjectModulation equations
dc.subjectNon-linear vibrations
dc.subjectPerturbation method
dc.subjectPrimary resonance
dc.subjectSolution algorithms
dc.subjectSteady state solution
dc.subjectTransverse vibrations
dc.subjectViscoelastic beams
dc.subjectEquations of motion
dc.titleA general solution procedure for the forced vibrations of a continuous system with cubic nonlinearities: Primary resonance case
dc.typeArticle

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