Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment

Lee, YS; Kerschen, G; Vakakis, AF; Panagopoulos, P; Bergman, L; McFarland, DM

dc.contributor.author	Lee, YS	en
dc.contributor.author	Kerschen, G	en
dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Panagopoulos, P	en
dc.contributor.author	Bergman, L	en
dc.contributor.author	McFarland, DM	en
dc.date.accessioned	2014-03-01T01:22:00Z
dc.date.available	2014-03-01T01:22:00Z
dc.date.issued	2005	en
dc.identifier.issn	0167-2789	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16436
dc.subject	Energy transfer	en
dc.subject	Essential nonlinearity	en
dc.subject	Resonance capture	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Physics, Multidisciplinary	en
dc.subject.classification	Physics, Mathematical	en
dc.subject.other	Computational complexity	en
dc.subject.other	Degrees of freedom (mechanics)	en
dc.subject.other	Energy transfer	en
dc.subject.other	Mathematical models	en
dc.subject.other	Mathematical transformations	en
dc.subject.other	Oscillators (electronic)	en
dc.subject.other	Problem solving	en
dc.subject.other	Essential nonlinearity	en
dc.subject.other	Linear oscillators	en
dc.subject.other	Nonlinear stiffness	en
dc.subject.other	Resonance capture	en
dc.subject.other	Nonlinear systems	en
dc.title	Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.physd.2005.03.014	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.physd.2005.03.014	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	We study the dynamics of a two-degree-of-freedom (DOF) nonlinear system consisting of a grounded linear oscillator coupled to a light mass by means of an essentially nonlinear (nonlinearizable) stiffness. We consider first the undamped system and perform a numerical study based on non-smooth transformations to determine its periodic solutions in a frequency-energy plot. It is found that there is a sequence of periodic solutions bifurcating or emanating from the main backbone curve of the plot. We then study analytically the periodic orbits of the undamped system using a complexification/averaging technique in order to determine the frequency contents of the various branches of solutions, and to understand the types of oscillation performed by the system at the different regimes of the motion. The transient responses of the weakly damped system are then examined, and numerical wavelet transforms are used to study the time evolutions of their harmonic components. We show that the structure of periodic orbits of the undamped system greatly influences the damped dynamics, as it causes complicated transitions between modes in the damped transient motion. In addition, there is the possibility of strong passive energy transfer (energy pumping) from the linear oscillator to the nonlinear attachment if certain periodic orbits of the undamped dynamics are excited by the initial conditions. (c) 2005 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Physica D: Nonlinear Phenomena	en
dc.identifier.doi	10.1016/j.physd.2005.03.014	en
dc.identifier.isi	ISI:000229713900003	en
dc.identifier.volume	204	en
dc.identifier.issue	1-2	en
dc.identifier.spage	41	en
dc.identifier.epage	69	en