Modelling of nonlinear modal interactions in the transient dynamics of an elastic rod with an essentially nonlinear attachment

Tsakirtzis, S; Lee, YS; Vakakis, AF; Bergman, LA; McFarland, DM

dc.contributor.author	Tsakirtzis, S	en
dc.contributor.author	Lee, YS	en
dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Bergman, LA	en
dc.contributor.author	McFarland, DM	en
dc.date.accessioned	2014-03-01T01:33:45Z
dc.date.available	2014-03-01T01:33:45Z
dc.date.issued	2010	en
dc.identifier.issn	1007-5704	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20575
dc.subject	Essential nonlinearity	en
dc.subject	Nonlinear modal interactions	en
dc.subject	System identification	en
dc.subject.classification	Literature, British Isles	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.classification	Physics, Fluids & Plasmas	en
dc.subject.classification	Physics, Mathematical	en
dc.subject.other	Dynamical interactions	en
dc.subject.other	Elastic rod	en
dc.subject.other	Empirical mode decomposition	en
dc.subject.other	Essential nonlinearity	en
dc.subject.other	Hilbert transform	en
dc.subject.other	Linear elastic	en
dc.subject.other	Linear oscillator	en
dc.subject.other	Multiscales	en
dc.subject.other	Non-parametric	en
dc.subject.other	Nonlinear modal interactions	en
dc.subject.other	Reduced order models	en
dc.subject.other	Resonant interaction	en
dc.subject.other	Strongly nonlinear	en
dc.subject.other	System identifications	en
dc.subject.other	Transient dynamics	en
dc.subject.other	Transient excitation	en
dc.subject.other	Nonlinear dynamical systems	en
dc.subject.other	Dynamical systems	en
dc.title	Modelling of nonlinear modal interactions in the transient dynamics of an elastic rod with an essentially nonlinear attachment	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.cnsns.2009.10.014	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.cnsns.2009.10.014	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	We perform system identification and modelling of the strongly nonlinear modal interactions in a system composed of a linear elastic rod with an essentially nonlinear attachment at its end. Our method is based on slow/fast decomposition of the transient dynamics of the system, combined with empirical mode decomposition (EMD) and Hilbert transforms. The derived reduced order models (ROMs) are in the form of sets of uncoupled linear oscillators (termed intrinsic modal oscillators - IMOs), each corresponding to a basic frequency of the dynamical interaction and forced by transient excitations that represent the nonlinear modal interactions between the rod and the attachment at each of these basic frequencies. A main advantage of our proposed technique is that it is nonparametric and multi-scale, so it is applicable to a broad range of linear as well as nonlinear dynamical systems. Moreover, it is computationally tractable and conceptually meaningful, and it leads to reduced order models of rather simple form that fully capture the basic strongly nonlinear resonant interactions between the subsystems of the problem. (C) 2009 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Communications in Nonlinear Science and Numerical Simulation	en
dc.identifier.doi	10.1016/j.cnsns.2009.10.014	en
dc.identifier.isi	ISI:000276821300042	en
dc.identifier.volume	15	en
dc.identifier.issue	9	en
dc.identifier.spage	2617	en
dc.identifier.epage	2633	en