A Degenerate bifurcation Structure in the Dynamics of Coupled Oscillators with Essential Stiffness Nonlinearities

Gendelman, O; Manevitch, LI; Vakakis, AF; Bergman, L

dc.contributor.author	Gendelman, O	en
dc.contributor.author	Manevitch, LI	en
dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Bergman, L	en
dc.date.accessioned	2014-03-01T01:18:31Z
dc.date.available	2014-03-01T01:18:31Z
dc.date.issued	2003	en
dc.identifier.issn	0924-090X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15057
dc.subject	Degenerate bifurcations	en
dc.subject	Essential stiffness nonlinearity	en
dc.subject	Nonlinear energy sink	en
dc.subject	Nonlinear normal modes	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Approximation theory	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Perturbation techniques	en
dc.subject.other	Resonance	en
dc.subject.other	Energy sink	en
dc.subject.other	Oscillators (electronic)	en
dc.title	A Degenerate bifurcation Structure in the Dynamics of Coupled Oscillators with Essential Stiffness Nonlinearities	en
heal.type	journalArticle	en
heal.identifier.primary	10.1023/A:1025515112708	en
heal.identifier.secondary	http://dx.doi.org/10.1023/A:1025515112708	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	We study the degenerate bifurcations of the nonlinear normal modes (NNMs) of an unforced system consisting of a linear oscillator weakly coupled to a nonlinear one that possesses essential stiffness nonlinearity. By defining the small coupling parameter e, we study the dynamics of this system at the limit epsilon --> 0. The degeneracy in the dynamics is manifested by a 'bifurcation from infinity' where a bifurcation point is generated at high energies, as perturbation of a state of infinite energy. Another (nondegenerate) bifurcation point is generated close to the point of exact 1:1 internal resonance between the linear and nonlinear oscillators. The degenerate bifurcation structure can be directly attributed to the high degeneracy of the uncoupled system in the limit e. 0, whose linearized structure possesses a double zero, and a conjugate pair of purely imaginary eigenvalues. First we construct local analytical approximations to the NNMs in the neighborhoods of the bifurcation points and at other energy ranges of the system. Then, we 'connect' the local approximations by global approximants, and identify global branches of NNMs where unstable and stable mode and inverse mode localization between the linear and nonlinear oscillators take place for decreasing energy.	en
heal.publisher	KLUWER ACADEMIC PUBL	en
heal.journalName	Nonlinear Dynamics	en
dc.identifier.doi	10.1023/A:1025515112708	en
dc.identifier.isi	ISI:000185124700001	en
dc.identifier.volume	33	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	10	en