Nonlinear dynamics of a system of coupled oscillators with essential stiffness nonlinearities

Vakakis, AF; Rand, RH

dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Rand, RH	en
dc.date.accessioned	2014-03-01T02:49:27Z
dc.date.available	2014-03-01T02:49:27Z
dc.date.issued	2003	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/34603
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-1842783116&partnerID=40&md5=0caed3a3698c099c8470ea316bfce1ac	en
dc.subject.other	Elliptical orbits (EO)	en
dc.subject.other	Resonant dynamics	en
dc.subject.other	Degrees of freedom (mechanics)	en
dc.subject.other	Oscillations	en
dc.subject.other	Oscillators (mechanical)	en
dc.subject.other	Stiffness	en
dc.subject.other	Trajectories	en
dc.subject.other	Dynamics	en
dc.title	Nonlinear dynamics of a system of coupled oscillators with essential stiffness nonlinearities	en
heal.type	conferenceItem	en
heal.publicationDate	2003	en
heal.abstract	We study the resonant dynamics of a two-degree-of-freedom system composed a linear oscillator weakly coupled to a strongly nonlinear one, with an essential (nonlinearizable) cubic stiffness nonlinearity. 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 (nonlinear 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 nonlinear energy pumping phenomena from the linear to the nonlinear 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.	en
heal.journalName	Proceedings of the ASME Design Engineering Technical Conference	en
dc.identifier.volume	5 B	en
dc.identifier.spage	1209	en
dc.identifier.epage	1220	en