Surprisingly complicated dynamics of a single-degree-of-freedom linear oscillator coupled to a nonlinear attachment

Lee, YS; Vakakis, AF; Panagopoulos, P; Kerschen, G; Bergman, LA; McFariand, DM

dc.contributor.author	Lee, YS	en
dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Panagopoulos, P	en
dc.contributor.author	Kerschen, G	en
dc.contributor.author	Bergman, LA	en
dc.contributor.author	McFariand, DM	en
dc.date.accessioned	2014-03-01T02:50:12Z
dc.date.available	2014-03-01T02:50:12Z
dc.date.issued	2005	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/34959
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-33144457802&partnerID=40&md5=fef333d49049354b7a9c9203b79ae0e4	en
dc.subject.other	Complexification/averaging technique	en
dc.subject.other	Frequency-energy plot	en
dc.subject.other	Linear oscillators	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	Degrees of freedom (mechanics)	en
dc.subject.other	Energy transfer	en
dc.subject.other	Linear systems	en
dc.subject.other	Mathematical transformations	en
dc.subject.other	Time varying systems	en
dc.subject.other	Nonlinear systems	en
dc.title	Surprisingly complicated dynamics of a single-degree-of-freedom linear oscillator coupled to a nonlinear attachment	en
heal.type	conferenceItem	en
heal.publicationDate	2005	en
heal.abstract	We study the dynamics of a two-degree-of-freedom nonlinear system consisting of a linear oscillator with an essentially nonlinear attachment. For the undamped system, we perform a numerical study based on non-smooth temporal transformations to determine its periodic solutions in a frequency-energy plot. It turns out that there is a sequence of periodic solutions bifurcating from the main backbone curve of the plot. We then study analytically the periodic orbits of the undamped system using the 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 from the linear oscillator to the nonlinear attachment if certain periodic orbits of the undamped dynamics are excited by the initial conditions. Copyright © 2005 by ASME.	en
heal.journalName	Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005	en
dc.identifier.volume	1 C	en
dc.identifier.spage	2485	en
dc.identifier.epage	2494	en