Transient resonant interactions of finite linear chains with essentially nonlinear end attachments leading to passive energy pumping

Panagopoulos, PN; Vakakis, AF; Tsakirtzis, S

dc.contributor.author	Panagopoulos, PN	en
dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Tsakirtzis, S	en
dc.date.accessioned	2014-03-01T01:21:39Z
dc.date.available	2014-03-01T01:21:39Z
dc.date.issued	2004	en
dc.identifier.issn	0020-7683	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16300
dc.subject	Critical Level	en
dc.subject	Elliptic Function	en
dc.subject	Integro-differential Equation	en
dc.subject	Oscillations	en
dc.subject	Perturbation Analysis	en
dc.subject	Phase Space	en
dc.subject	Transient Dynamics	en
dc.subject	Multiple Degree of Freedom	en
dc.subject.classification	Mechanics	en
dc.subject.other	Linear oscillators	en
dc.subject.other	Nonlinear energy pumping	en
dc.subject.other	Structural modification	en
dc.subject.other	Transient resonance	en
dc.subject.other	Approximation theory	en
dc.subject.other	Damping	en
dc.subject.other	Degrees of freedom (mechanics)	en
dc.subject.other	Differential equations	en
dc.subject.other	Energy management	en
dc.subject.other	Functions	en
dc.subject.other	Integral equations	en
dc.subject.other	Mathematical models	en
dc.subject.other	Perturbation techniques	en
dc.subject.other	Resonance	en
dc.subject.other	Stiffness matrix	en
dc.subject.other	Transients	en
dc.subject.other	Vibration control	en
dc.subject.other	Structural analysis	en
dc.title	Transient resonant interactions of finite linear chains with essentially nonlinear end attachments leading to passive energy pumping	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijsolstr.2004.05.005	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijsolstr.2004.05.005	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	We study resonance capture phenomena leading to energy pumping in systems with multiple degrees of freedom (DOF), composed of N linear oscillators weakly coupled to strongly nonlinear attachments possessing essential (nonlinearizable) cubic stiffness nonlinearities. First we present numerical evidence of energy pumping in the systems under consideration, i.e., of passive, one-way (irreversible) transfer of externally imparted energy to the nonlinear attachments, provided that the energy is above a critical level. To obtain a better understanding of the energy pumping phenomenon we reduce the dynamics governing the chain-attachment interaction to a single, nonlinear integro-differential equation that governs exactly the transient dynamics of the strongly nonlinear attachment. By introducing an approximation based on Jacobian elliptic functions we derive an approximate set of two nonlinear integro-differential modulation equations that govern the time evolution of the amplitude and phase of the motion of the attachment. This set of modulation equations is studied both analytically and numerically. We then perform a perturbation analysis in an O(rootepsilon) neighborhood of a 1:1 resonant manifold of the system in order to study the attracting region in the reduced phase space of the system, that is responsible for resonance capture and nonlinear energy pumping. This analysis provides a justification of the numerical findings. (C) 2004 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Solids and Structures	en
dc.identifier.doi	10.1016/j.ijsolstr.2004.05.005	en
dc.identifier.isi	ISI:000224136100025	en
dc.identifier.volume	41	en
dc.identifier.issue	22-23	en
dc.identifier.spage	6505	en
dc.identifier.epage	6528	en