Transient dynamics of a dispersive elastic wave guide weakly coupled to an essentially nonlinear end attachment

Vakakis, AF; Manevitch, LI; Musienko, AI; Kerschen, G; Bergman, LA

dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Manevitch, LI	en
dc.contributor.author	Musienko, AI	en
dc.contributor.author	Kerschen, G	en
dc.contributor.author	Bergman, LA	en
dc.date.accessioned	2014-03-01T01:23:17Z
dc.date.available	2014-03-01T01:23:17Z
dc.date.issued	2005	en
dc.identifier.issn	0165-2125	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16882
dc.subject	Nonlinear resonant interactions of traveling waves	en
dc.subject	Resonance capture	en
dc.subject.classification	Acoustics	en
dc.subject.classification	Mechanics	en
dc.subject.classification	Physics, Multidisciplinary	en
dc.subject.other	Cascade control systems	en
dc.subject.other	Computer simulation	en
dc.subject.other	Differential equations	en
dc.subject.other	Green's function	en
dc.subject.other	Integral equations	en
dc.subject.other	Phase modulation	en
dc.subject.other	Infinite sets	en
dc.subject.other	Linear rods	en
dc.subject.other	Neumann expansions	en
dc.subject.other	Resonance capture cascades	en
dc.subject.other	Elastic waves	en
dc.subject.other	Green function	en
dc.subject.other	wave propagation	en
dc.title	Transient dynamics of a dispersive elastic wave guide weakly coupled to an essentially nonlinear end attachment	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.wavemoti.2004.06.002	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.wavemoti.2004.06.002	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	We consider the dynamics of a dispersive semi-infinite linear rod weakly connected to an essentially nonlinear end attachment. Using a Green's function formulation we reduce the dynamics to an integro-differential equation, which we express in the form of an infinite set of ordinary differential equations using Neumann expansions. We examine resonant interactions of the attachment with incident traveling waves propagating in the pass band of the rod, as well as resonance capture phenomena where the attachment engages in transient 1:1 internal resonance with the in-phase mode of the rod, at the bounding frequency of its pass and stop bands. The studied resonant interactions of the nonlinear attachment with traveling waves are similar to resonance capture cascades occurring in finite-chain nonlinear attachment configurations; these are the transient dynamics of the attachment as it engages in a series of instantaneous resonances with a continuous spectrum of frequencies in the pass band of the medium. As the energy of the attachment decreases due to damping and energy radiation back to the rod, the attachment engages in 1:1 resonance capture with the in-phase mode of the rod; this resonance capture occurs due to the dispersion property in the linear medium. It is shown that the transient dynamics of resonance capture can be reduced to a set of two 'slow flow' amplitude and phase modulation equations. The analytical results are in agreement with direct numerical simulations. (C) 2004 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Wave Motion	en
dc.identifier.doi	10.1016/j.wavemoti.2004.06.002	en
dc.identifier.isi	ISI:000225304000002	en
dc.identifier.volume	41	en
dc.identifier.issue	2	en
dc.identifier.spage	109	en
dc.identifier.epage	132	en