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

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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 http://hdl.handle.net/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.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

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