Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1:1 resonance captures: Part I

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dc.contributor.author Quinn, DD en
dc.contributor.author Gendelman, O en
dc.contributor.author Kerschen, G en
dc.contributor.author Sapsis, TP en
dc.contributor.author Bergman, LA en
dc.contributor.author Vakakis, AF en
dc.date.accessioned 2014-03-01T01:28:14Z
dc.date.available 2014-03-01T01:28:14Z
dc.date.issued 2008 en
dc.identifier.issn 0022-460X en
dc.identifier.uri http://hdl.handle.net/123456789/18770
dc.subject.classification Acoustics en
dc.subject.classification Engineering, Mechanical en
dc.subject.classification Mechanics en
dc.subject.other Computational methods en
dc.subject.other Damping en
dc.subject.other Energy transfer en
dc.subject.other Hamiltonians en
dc.subject.other Linear systems en
dc.subject.other Phase transitions en
dc.subject.other Broadband energy en
dc.subject.other Hamiltonian dynamics en
dc.subject.other Nonlinear oscillators en
dc.subject.other Passive energy transfer en
dc.subject.other Oscillators (electronic) en
dc.title Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1:1 resonance captures: Part I en
heal.type journalArticle en
heal.identifier.primary 10.1016/j.jsv.2007.10.026 en
heal.identifier.secondary http://dx.doi.org/10.1016/j.jsv.2007.10.026 en
heal.language English en
heal.publicationDate 2008 en
heal.abstract We study targeted energy transfers and nonlinear transitions in the damped dynamics of a two degree-of-freedom system of coupled oscillators (a linear oscillator with a lightweight, essentially nonlinear, ungrounded attachment), caused by 1: 1 resonance captures of the dynamics. Part I of this work deals with the underlying structure of the Hamiltonian dynamics of the system, and demonstrates that, for sufficiently small values of viscous damping, the damped transitions are strongly influenced by the underlying topological structure of periodic and quasiperiodic orbits of the corresponding Hamiltonian system. Focusing exclusively on 1:1 resonance captures in the system, it is shown that the topology of these damped transitions affect drastically the efficiency of passive energy transfer from the linear system to the nonlinear attachment. Then, a detailed computational study of the different types of nonlinear transitions that occur in the weakly damped system is presented, together with an analytical treatment of the nonlinear stability of certain families of periodic solutions of the underlying Hamiltonian system that strongly influence the said transitions. As a result of these studies, conditions on the system and forcing parameters that lead to effective or even optimal energy transfer from the linear system to the nonlinear attachment are determined. In Part 11 of this work, direct analytical treatment of the governing strongly nonlinear damped equations of motion is performed, in order to analytically model the dynamics in the region of optimal energy transfer, and to determine the characteristic time scales of the dynamics that influence the capacity of the nonlinear attachment to passively absorb and locally dissipate broadband energy from the linear oscillator. (c) 2007 Elsevier Ltd. All rights reserved. en
heal.journalName Journal of Sound and Vibration en
dc.identifier.doi 10.1016/j.jsv.2007.10.026 en
dc.identifier.isi ISI:000253872300039 en
dc.identifier.volume 311 en
dc.identifier.issue 3-5 en
dc.identifier.spage 1228 en
dc.identifier.epage 1248 en

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