Karhunen-Loeve analysis and order reduction of the transient dynamics of linear coupled oscillators with strongly nonlinear end attachments

Ma, X; Vakakis, AF; Bergman, LA

dc.contributor.author	Ma, X	en
dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Bergman, LA	en
dc.date.accessioned	2014-03-01T01:28:43Z
dc.date.available	2014-03-01T01:28:43Z
dc.date.issued	2008	en
dc.identifier.issn	0022-460X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18934
dc.subject.classification	Acoustics	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Decomposition	en
dc.subject.other	Degrees of freedom (mechanics)	en
dc.subject.other	Energy absorption	en
dc.subject.other	Energy transfer	en
dc.subject.other	Nonlinear systems	en
dc.subject.other	Oscillators (electronic)	en
dc.subject.other	Correlation coefficient (MCC)	en
dc.subject.other	Karhunen-Loeve analysis	en
dc.subject.other	Nonlinear attachment	en
dc.subject.other	Nonlinear energy-pumping	en
dc.subject.other	Dynamical systems	en
dc.title	Karhunen-Loeve analysis and order reduction of the transient dynamics of linear coupled oscillators with strongly nonlinear end attachments	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jsv.2007.07.053	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jsv.2007.07.053	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	The Karhunen-Loeve (K-L) decomposition method has become a popular technique to create low-dimensional, reduced-order models of dynamical systems. In this paper this technique is applied to a multi-degree-of-freedom chain of linear coupled oscillators with a strongly nonlinear (nonlinearizable), lightweight end attachment. By performing K L decomposition we show that the lightweight nonlinear attachment (possessing 0.5% of the total mass of the chain) can affect the global dynamics of the linear chain, exhibiting nonlinear energy-pumping phenomena; that is, irreversible passive targeted energy transfers from the linear chain to the nonlinear end attachment, where this energy is locally confined and dissipated without 'spreading back' to the primary system. It is shown that the occurrence of energy pumping can be identified by studying the dominant K-L modes of the dynamics, as well as, the energy distribution among them. Moreover, by comparing the action of the strongly nonlinear attachment to the classical linear vibration absorber, we show robustness of passive nonlinear energy absorption over wide parameter ranges. On the other hand, the case-sensitive nature of K L-based reduced-order models has always been a constraint for K-L decomposition, since one cannot quantify a priori the error bound of such low-dimensional reduced-order models when different initial conditions are applied to the system. To alleviate this constraint, the paper proposes a multiple correlation coefficient (MCC) as a quantitative measure to effectively assess the applicability of a K-L-based reduced-order model derived for a specific set of initial conditions to a small neighborhood of initial conditions containing that initial state. The derived reduced-order models are validated through reconstruction of the system responses and comparisons to direct numerical integrations. (c) 2007 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.2007.07.053	en
dc.identifier.isi	ISI:000251627500010	en
dc.identifier.volume	309	en
dc.identifier.issue	3-5	en
dc.identifier.spage	569	en
dc.identifier.epage	587	en