Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances

dc.contributor.authorNayfeh, Ali H.en
dc.contributor.authorArafat, Haider N.en
dc.contributor.departmentBiomedical Engineering and Mechanicsen
dc.date.accessioned2017-09-18T10:10:34Zen
dc.date.available2017-09-18T10:10:34Zen
dc.date.issued1998-01-01en
dc.date.updated2017-09-18T10:10:34Zen
dc.description.abstractThe nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.en
dc.description.versionPublished versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationAli H. Nayfeh and Haider N. Arafat, “Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances,” Shock and Vibration, vol. 5, no. 5-6, pp. 277-288, 1998. doi:10.1155/1998/181460en
dc.identifier.doihttps://doi.org/10.1155/1998/181460en
dc.identifier.urihttp://hdl.handle.net/10919/79112en
dc.language.isoenen
dc.publisherHindawien
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.holderCopyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.en
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.titleNonlinear Response of Cantilever Beams to Combination and Subcombination Resonancesen
dc.title.serialShock and Vibrationen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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