Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1:1 resonance captures: Part II, analytical study

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

dc.contributor.author	Sapsis, TP	en
dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Gendelman, OV	en
dc.contributor.author	Bergman, LA	en
dc.contributor.author	Kerschen, G	en
dc.contributor.author	Quinn, DD	en
dc.date.accessioned	2014-03-01T01:30:18Z
dc.date.available	2014-03-01T01:30:18Z
dc.date.issued	2009	en
dc.identifier.issn	0022-460X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19542
dc.subject.classification	Acoustics	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Analytical predictions	en
dc.subject.other	Analytical treatment	en
dc.subject.other	Broadband energy	en
dc.subject.other	Characteristic time	en
dc.subject.other	Damped systems	en
dc.subject.other	Energy transfer efficiency	en
dc.subject.other	Hamiltonian dynamics	en
dc.subject.other	Hamiltonian systems	en
dc.subject.other	Homoclinic orbits	en
dc.subject.other	Initial energy	en
dc.subject.other	Linear oscillator	en
dc.subject.other	Non-linear oscillators	en
dc.subject.other	Nonlinear energy sink	en
dc.subject.other	Parameter regions	en
dc.subject.other	Quasi-periodic	en
dc.subject.other	Resonance capture	en
dc.subject.other	Strongly nonlinear	en
dc.subject.other	Time-scale	en
dc.subject.other	Topological structure	en
dc.subject.other	Transient resonance	en
dc.subject.other	Transient response	en
dc.subject.other	Two-degree-of-freedom	en
dc.subject.other	Viscous damping	en
dc.subject.other	Biped locomotion	en
dc.subject.other	Dynamics	en
dc.subject.other	Energy transfer	en
dc.subject.other	Equations of motion	en
dc.subject.other	Hamiltonians	en
dc.subject.other	Meats	en
dc.subject.other	Nonlinear control systems	en
dc.subject.other	Orbits	en
dc.subject.other	Oscillators (electronic)	en
dc.subject.other	Oscillators (mechanical)	en
dc.subject.other	Resonance	en
dc.subject.other	Structural optimization	en
dc.subject.other	Nonlinear equations	en
dc.title	Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1:1 resonance captures: Part II, analytical study	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jsv.2009.03.004	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jsv.2009.03.004	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	We study targeted energy transfer in a two degree-of-freedom damped system under the condition of 1:1 transient resonance capture. The system consists of a linear oscillator strongly coupled to an essentially nonlinear attachment or nonlinear energy sink. In a companion paper [Quinn et al., Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1:1 resonance captures: part I, Journal of Sound and Vibration 311 (2008) 1228-1248] we studied the underlying structure of the Hamiltonian dynamics of this system, and showed that for sufficiently small values of viscous damping, nonlinear damped transitions are strongly influenced by the underlying topological structure of periodic and quasiperiodic orbits of the Hamiltonian system. In this work direct analytical treatment of the governing strongly nonlinear damped equations of motion is performed through slow/fast partitions of the transient responses, in order to investigate analytically the parameter region of optimal targeted energy transfer. To this end, we 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. Then, we prove that optimal targeted energy transfer is realized for initial energies close to the neighborhood of a homoclinic orbit of the underlying Hamiltonian system. We study analytically transient orbits resulting as perturbations of the homoclinic orbit in the weakly damped system, and show that this yields an additional slow-time scale in the averaged dynamics, and leads to optimal targeted energy transfer from the linear oscillator to the nonlinear energy sink in a single ""super-slow"" half-cycle. We show that at higher energies, this ""super-slow"" half-cycle is replaced by strong nonlinear beats, which lead to significant but suboptimal targeted energy transfer efficiency. Finally, we investigate numerically targeted energy transfer efficiency in this system over a wide range of system parameters and verify the analytical predictions. © 2009 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.2009.03.004	en
dc.identifier.isi	ISI:000267679800019	en
dc.identifier.volume	325	en
dc.identifier.issue	1-2	en
dc.identifier.spage	297	en
dc.identifier.epage	320	en