Dynamics of linear discrete systems connected to local, essentially non-linear attachments

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

dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Manevitch, LI	en
dc.contributor.author	Gendelman, O	en
dc.contributor.author	Bergman, L	en
dc.date.accessioned	2014-03-01T01:18:54Z
dc.date.available	2014-03-01T01:18:54Z
dc.date.issued	2003	en
dc.identifier.issn	0022-460X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15255
dc.subject	Analytic Continuation	en
dc.subject	Coupled Oscillator	en
dc.subject	Discrete System	en
dc.subject	Normal Modes	en
dc.subject	Point of View	en
dc.subject.classification	Acoustics	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Energy transfer	en
dc.subject.other	Solitons	en
dc.subject.other	Topology	en
dc.subject.other	Energy pumping	en
dc.subject.other	Linear systems	en
dc.title	Dynamics of linear discrete systems connected to local, essentially non-linear attachments	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0022-460X(02)01207-5	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0022-460X(02)01207-5	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	The dynamics of a linear periodic substructure, weakly coupled to an essentially non-linear attachment are studied. The essential (non-linearizable) non-linearity of the attachment enables it to resonate with any of the linearized modes of the subtructure leading to energy pumping phenomena, e.g., passive, one-way, irreversible transfer of energy from the substructure to the attachment. As a specific application the dynamics of a finite linear chain of coupled oscillators with a non-linear end attachment is examined. In the absence of damping, it is found that the dynamical effect of the non-linear attachment is predominant in neighborhoods of internal resonances between the attachment and the chain. When damping exists energy pumping phenomena are realized in the system. It is shown that energy pumping strongly depends on the topological structure of the non-linear normal modes (NNMs) of the underlying undamped system. This is due to the fact that energy pumping is caused by the excitation of certain damped invariant NNM manifolds that are analytic continuations for weak damping of NNMs of the underlying undamped system. The bifurcations of the NNMs of the undamped system help explain resonance capture cascades in the damped system. This is a series of energy pumping phenomena occurring at different frequencies, with sudden lower frequency transitions between sequential events. The observed multi-frequency energy pumping cascades are particularly interesting from a practical point of view, since they indicate that nonlinear attachments can be designed to resonate and extract energy from an a priori specified set of modes of a linear structure, in compatibility with the design objectives. (C) 2002 Elsevier Science Ltd. All rights reserved.	en
heal.publisher	ACADEMIC PRESS LTD ELSEVIER SCIENCE LTD	en
heal.journalName	Journal of Sound and Vibration	en
dc.identifier.doi	10.1016/S0022-460X(02)01207-5	en
dc.identifier.isi	ISI:000183872000004	en
dc.identifier.volume	264	en
dc.identifier.issue	3	en
dc.identifier.spage	559	en
dc.identifier.epage	577	en