General solution algorithm for three-to-one internal resonances of a cubic nonlinear vibration model

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dc.contributor.authorÖzhan B.B.
dc.contributor.authorPakdemirli M.
dc.date.accessioned2024-07-22T08:21:27Z
dc.date.available2024-07-22T08:21:27Z
dc.date.issued2009
dc.description.abstractA generalized nonlinear vibration model of continuous systems is considered. The model includes arbitrary linear and cubic differential and/or integral operators. Linear operators represent the linear parts and cubic operators represent the nonlinear parts of the model. The generalized equation of motion is analyzed by using the method of multiple scales (a perturbation method). Three-to-one internal resonances between natural frequencies are obtained. The amplitude and phase modulation equations are presented. Approximate solution is derived. Steady state solutions and their stability are discussed. Solution algorithm is applied to nonlinear vibration model of an axially moving Euler Bernoulli beam. Constant velocity case of axially moving beam is analyzed. Natural frequencies of beam are given for different velocity values. Steady state solutions and their stability are determined numerically. Frequency response relations are obtained. Energy transfer of one mode to another via a three-to-one internal resonance is observed. Jump phenomena of the system are shown graphically by choosing different vibration and beam parameter values.
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/18619
dc.language.isoEnglish
dc.subjectEnergy transfer
dc.subjectEquations of motion
dc.subjectFrequency response
dc.subjectMathematical operators
dc.subjectNatural frequencies
dc.subjectPhase modulation
dc.subjectApproximate solution
dc.subjectAxially moving beams
dc.subjectBeam parameter
dc.subjectConstant velocities
dc.subjectContinuous system
dc.subjectEuler Bernoulli beams
dc.subjectGeneral solutions
dc.subjectGeneralized Equations
dc.subjectIntegral operators
dc.subjectInternal resonance
dc.subjectJump phenomenon
dc.subjectLinear operators
dc.subjectMethod of multiple scale
dc.subjectModulation equations
dc.subjectNon-linear vibrations
dc.subjectPerturbation method
dc.subjectSolution algorithms
dc.subjectSteady state solution
dc.subjectAlgorithms
dc.titleGeneral solution algorithm for three-to-one internal resonances of a cubic nonlinear vibration model
dc.typeConference paper

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