Complex dynamics and targeted energy transfer in linear oscillators coupled to multi-degree-of-freedom essentially nonlinear attachments

Tsakirtzis, S; Panagopoulos, PN; Kerschen, G; Gendelman, O; Vakakis, AF; Bergman, LA

dc.contributor.author	Tsakirtzis, S	en
dc.contributor.author	Panagopoulos, PN	en
dc.contributor.author	Kerschen, G	en
dc.contributor.author	Gendelman, O	en
dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Bergman, LA	en
dc.date.accessioned	2014-03-01T01:26:02Z
dc.date.available	2014-03-01T01:26:02Z
dc.date.issued	2007	en
dc.identifier.issn	0924-090X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17889
dc.subject	Essentially nonlinear attachments	en
dc.subject	Passive targeted energy transfer	en
dc.subject	Regular backbone branches	en
dc.subject	Singular backbone branches	en
dc.subject	Transient resonance captures	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Degrees of freedom (mechanics)	en
dc.subject.other	Energy transfer	en
dc.subject.other	Hamiltonians	en
dc.subject.other	Linear systems	en
dc.subject.other	Parameter estimation	en
dc.subject.other	Time varying systems	en
dc.subject.other	Essentially nonlinear attachments	en
dc.subject.other	Passive targeted energy transfer	en
dc.subject.other	Regular backbone branches	en
dc.subject.other	Singular backbone branches	en
dc.subject.other	Transient resonance captures	en
dc.subject.other	Oscillators (mechanical)	en
dc.title	Complex dynamics and targeted energy transfer in linear oscillators coupled to multi-degree-of-freedom essentially nonlinear attachments	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s11071-006-9089-x	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s11071-006-9089-x	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment can passively absorb broadband energy from the linear system in a one-way, irreversible fashion, acting in essence as nonlinear energy sink (NES). Strong passive targeted energy transfer from the linear to the nonlinear subsystem is possible over wide frequency and energy ranges. In an effort to study the dynamics of the coupled system of oscillators, we study numerically and analytically the periodic orbits of the corresponding undamped and unforced hamiltonian system with asymptotics and reduction. We prove the existence of a family of countable infinity of periodic orbits that result from combined parametric and external resonance interactions of the masses of the NES. We numerically demonstrate that the topological structure of the periodic orbits in the frequency-energy plane of the hamiltonian system greatly influences the strength of targeted energy transfer in the damped system and, to a great extent, governs the overall transient damped dynamics. This work may be regarded as a contribution towards proving the efficacy the utilizing essentially nonlinear attachments as passive broadband boundary controllers. © Springer Science+Business Media, Inc. 2007.	en
heal.publisher	SPRINGER	en
heal.journalName	Nonlinear Dynamics	en
dc.identifier.doi	10.1007/s11071-006-9089-x	en
dc.identifier.isi	ISI:000244200100004	en
dc.identifier.volume	48	en
dc.identifier.issue	3	en
dc.identifier.spage	285	en
dc.identifier.epage	318	en