Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances

Nayfeh, Ali H.; Arafat, Haider N.

Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances

dc.contributor.author	Nayfeh, Ali H.	en
dc.contributor.author	Arafat, Haider N.	en
dc.contributor.department	Biomedical Engineering and Mechanics	en
dc.date.accessioned	2017-09-18T10:10:34Z	en
dc.date.available	2017-09-18T10:10:34Z	en
dc.date.issued	1998-01-01	en
dc.date.updated	2017-09-18T10:10:34Z	en
dc.description.abstract	The 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.version	Published version	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	Ali 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:10.1155/1998/181460	en
dc.identifier.doi	https://doi.org/10.1155/1998/181460	en
dc.identifier.uri	http://hdl.handle.net/10919/79112	en
dc.language.iso	en	en
dc.publisher	Hindawi	en
dc.rights	Creative Commons Attribution 4.0 International	en
dc.rights.holder	Copyright © 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.uri	http://creativecommons.org/licenses/by/4.0/	en
dc.title	Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances	en
dc.title.serial	Shock and Vibration	en
dc.type	Article - Refereed	en
dc.type.dcmitype	Text	en