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

Quinn, DD; Gendelman, O; Kerschen, G; Sapsis, TP; Bergman, LA; Vakakis, AF

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	https://dspace.lib.ntua.gr/xmlui/handle/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.publisher	ACADEMIC PRESS LTD ELSEVIER SCIENCE LTD	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