Nonlinear Vibration Movements of the Mid-Supported Micro-Beam

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dc.contributor.authorAkkoca S.
dc.contributor.authorBaǧdatli S.M.
dc.contributor.authorKara Toǧun N.
dc.date.accessioned2024-07-22T08:04:03Z
dc.date.available2024-07-22T08:04:03Z
dc.date.issued2022
dc.description.abstractThis study analyzes the vibration movements of multi-support micro beams placed in an electrically smooth area using the modified couple stress theory. It has been assumed that the potential voltage that creates the electrical field strength varies harmonically. Large number of experiments in recent years have indicated that classical continuum theory is unable to predict the mechanical behavior of microstructure with small size. However, nonclassical continuum theory should be used to accurately design and analyze the microstructures. Modified couple stress theory models the micro and nanomechanical systems with higher accuracy because they employ additional material parameters to the equation considering size dependent behavior. The most general nonlinear motion equations for multi-support microbeams have been obtained by considering the material size parameter, the number of support and support positions, damping effect, axial stresses, electrical field strength, and nonlinear effects resulting from elongations. The nonlinear equations of motion are obtained according to the Hamilton method using the modified couple stress theory (MCST). The resulting equations of motion are nondimensionalized. In this way, the mathematical model has been made independent of the type and geometric structure of the material. Approximate solutions of the obtained dimensionless motion equation are obtained by the multi-scale method, which is one of the perturbation methods. As a result, an increase occurs in the first mode frequencies (ω1) and nonlinear correction effect parameters (λ(ω1)) with the progress of the center support position gradually towards η=0.5 and the increase of the microbeam elasticity coefficient (α2). © 2022 World Scientific Publishing Company.
dc.identifier.DOI-ID10.1142/S0219455422501747
dc.identifier.issn02194554
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/12551
dc.language.isoEnglish
dc.publisherWorld Scientific
dc.subjectContinuum mechanics
dc.subjectMicrostructure
dc.subjectNonlinear equations
dc.subjectPerturbation techniques
dc.subjectVibration analysis
dc.subjectElectrical field strength
dc.subjectEquation of motion
dc.subjectMicro beams
dc.subjectMiddle-supported
dc.subjectModified couple stress theories
dc.subjectMulti support
dc.subjectNon-linear vibrations
dc.subjectPerturbation method
dc.subjectPotential voltage
dc.subjectVibration
dc.subjectEquations of motion
dc.titleNonlinear Vibration Movements of the Mid-Supported Micro-Beam
dc.typeArticle

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