Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass

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dc.contributor.authorÖzkaya E.
dc.contributor.authorSarigül M.
dc.contributor.authorBoyaci H.
dc.date.accessioned2024-07-22T08:21:26Z
dc.date.available2024-07-22T08:21:26Z
dc.date.issued2009
dc.description.abstractIn this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonlinear vibrations were investigated. Sinusoidal and parabolic type functions were used as curvature functions. Equations of motion have cubic nonlinearities because of elongations during vibrations. Damping and harmonic excitation terms were added to the equations of motion. Method of multiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequencies were calculated exactly for different mass ratios, mass locations, curvature functions, and linear elastic foundation coefficients. Amplitude-phase modulation equations were found by considering primary resonance case. Effects of nonlinear terms on natural frequencies were calculated. Frequency-amplitude and frequency-response graphs were plotted. Finally effects of concentrated mass and chosen curvature function on nonlinear vibrations were investigated. © 2009 The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH.
dc.identifier.DOI-ID10.1007/s10409-009-0275-1
dc.identifier.issn05677718
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/18610
dc.language.isoEnglish
dc.subjectControl nonlinearities
dc.subjectCurved beams and girders
dc.subjectFoundations
dc.subjectFrequency response
dc.subjectIntegrodifferential equations
dc.subjectMechanics
dc.subjectNatural frequencies
dc.subjectPerturbation techniques
dc.subjectConcentrated mass
dc.subjectCubic nonlinearities
dc.subjectCurvature function
dc.subjectCurved beams
dc.subjectDifferent mass
dc.subjectElastic foundation
dc.subjectEuler Bernoulli beams
dc.subjectHarmonic excitation
dc.subjectLinear elastic
dc.subjectMethod of multiple scale
dc.subjectNon-linear vibrations
dc.subjectNonlinear elastic foundation
dc.subjectNonlinear terms
dc.subjectNonlinear transverse vibration
dc.subjectPrimary resonance
dc.subjectSimply supported
dc.subjectEquations of motion
dc.titleNonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass
dc.typeArticle

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