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Article: Various Bifurcation Phenomena in a Nonlinear Curved Beam Subjected to Base Harmonic Excitation

TitleVarious Bifurcation Phenomena in a Nonlinear Curved Beam Subjected to Base Harmonic Excitation
Authors
Issue Date2018
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD.
Citation
International Journal of Bifurcation and Chaos, 2018, v. 28, p. 1830023 How to Cite?
AbstractVarious bifurcation phenomena in a nonlinear curved beam subjected to base harmonic excitation, which is governed by a coupled nonlinear equation with both quadratic and cubic nonlinearities, are investigated using the incremental harmonic balance (IHB) method. The nonlinear partial differential equation that governs the motion of the curved beam is given using Hamilton's principle. A spatially discretized governing equation is derived using Galerkin's method, yielding a set of second-order nonlinear ordinary different equations. A high-dimensional model that can take nonlinear model coupling into account is derived. Specific attention is paid to the different bifurcation phenomena of frequency responses and amplitude responses of the system without and with an anti-symmetric mode being excited. Numerical results reveal the rich and interesting diverse bifurcation phenomena that have not been presented in the existent literature on the nonlinear vibration of the curved beam system. Saddle-node, Hopf, and period-doubling bifurcations are observed without an anti-symmetric mode being excited. Besides, a symmetry-breaking bifurcation is observed with an anti-symmetric mode being excited. Furthermore, the phase portraits and bifurcation points obtained by the IHB method agree very well with those obtained by the numerical integration using the fourth-order Runge-Kutta method.
Persistent Identifierhttp://hdl.handle.net/10722/259174
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorHuang, JL-
dc.contributor.authorSu, KL-
dc.contributor.authorLee, RYY-
dc.contributor.authorChen, SH-
dc.date.accessioned2018-09-03T04:02:42Z-
dc.date.available2018-09-03T04:02:42Z-
dc.date.issued2018-
dc.identifier.citationInternational Journal of Bifurcation and Chaos, 2018, v. 28, p. 1830023-
dc.identifier.urihttp://hdl.handle.net/10722/259174-
dc.description.abstractVarious bifurcation phenomena in a nonlinear curved beam subjected to base harmonic excitation, which is governed by a coupled nonlinear equation with both quadratic and cubic nonlinearities, are investigated using the incremental harmonic balance (IHB) method. The nonlinear partial differential equation that governs the motion of the curved beam is given using Hamilton's principle. A spatially discretized governing equation is derived using Galerkin's method, yielding a set of second-order nonlinear ordinary different equations. A high-dimensional model that can take nonlinear model coupling into account is derived. Specific attention is paid to the different bifurcation phenomena of frequency responses and amplitude responses of the system without and with an anti-symmetric mode being excited. Numerical results reveal the rich and interesting diverse bifurcation phenomena that have not been presented in the existent literature on the nonlinear vibration of the curved beam system. Saddle-node, Hopf, and period-doubling bifurcations are observed without an anti-symmetric mode being excited. Besides, a symmetry-breaking bifurcation is observed with an anti-symmetric mode being excited. Furthermore, the phase portraits and bifurcation points obtained by the IHB method agree very well with those obtained by the numerical integration using the fourth-order Runge-Kutta method.-
dc.languageeng-
dc.publisherWORLD SCIENTIFIC PUBL CO PTE LTD. -
dc.relation.ispartofInternational Journal of Bifurcation and Chaos-
dc.titleVarious Bifurcation Phenomena in a Nonlinear Curved Beam Subjected to Base Harmonic Excitation-
dc.typeArticle-
dc.identifier.emailSu, KL: klsu@hkucc.hku.hk-
dc.identifier.authoritySu, KL=rp00072-
dc.identifier.doi10.1142/S0218127418300239-
dc.identifier.hkuros287766-
dc.identifier.volume28-
dc.identifier.spage1830023-
dc.identifier.epage1830023-
dc.identifier.isiWOS:000439096400003-
dc.publisher.placeSingapore-

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