Non-linear dynamics of a system of coupled oscillators with essential stiffness non-linearities

Vakakis, AF; Rand, RH

dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Rand, RH	en
dc.date.accessioned	2014-03-01T01:21:08Z
dc.date.available	2014-03-01T01:21:08Z
dc.date.issued	2004	en
dc.identifier.issn	0020-7462	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16084
dc.subject	Capture	en
dc.subject	Coupled oscillators	en
dc.subject	Non-linear	en
dc.subject	Resonance	en
dc.subject.classification	Mechanics	en
dc.subject.other	Damping	en
dc.subject.other	Degrees of freedom (mechanics)	en
dc.subject.other	Energy transfer	en
dc.subject.other	Nonlinear systems	en
dc.subject.other	Oscillations	en
dc.subject.other	Vibrations (mechanical)	en
dc.subject.other	Energy pumping	en
dc.subject.other	Oscillators (mechanical)	en
dc.title	Non-linear dynamics of a system of coupled oscillators with essential stiffness non-linearities	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0020-7462(03)00098-2	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0020-7462(03)00098-2	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	We study the resonant dynamics of a two-degree-of-freedom system composed of a linear oscillator weakly coupled to a strongly non-linear one, with an essential (non-linearizable) cubic stiffness non-linearity. For the undamped system this leads to a series of internal resonances, depending on the level of (conserved) total energy of oscillation. We study in detail the 1:1 internal resonance, and show that the undamped system possesses stable and unstable synchronous periodic motions (non-linear normal modes - NNMs), as well as, asynchronous periodic motions (elliptic orbits - EOs). Furthermore, we show that when damping is introduced certain NNMs produce resonance capture phenomena, where a trajectory of the damped dynamics gets 'captured' in the neighborhood of a damped NNM before 'escaping' and becoming an oscillation with exponentially decaying amplitude. In turn, these resonance captures may lead to passive non-linear energy pumping phenomena from the linear to the non-linear oscillator. Thus, sustained resonance capture appears to provide a dynamical mechanism for passively transferring energy from one part of the system to another, in a one-way, irreversible fashion. Numerical integrations confirm the analytical predictions. © 2003 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Non-Linear Mechanics	en
dc.identifier.doi	10.1016/S0020-7462(03)00098-2	en
dc.identifier.isi	ISI:000220480200002	en
dc.identifier.volume	39	en
dc.identifier.issue	7	en
dc.identifier.spage	1079	en
dc.identifier.epage	1091	en