A POD-based identification of the reduced dynamics of an exact nonlinear rod loaded transversely

Georgiou, IT; Kanavis, CE

dc.contributor.author	Georgiou, IT	en
dc.contributor.author	Kanavis, CE	en
dc.date.accessioned	2014-03-01T02:49:22Z
dc.date.available	2014-03-01T02:49:22Z
dc.date.issued	2003	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/34554
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-1842682305&partnerID=40&md5=0cc655fd4832702d764f466f338bedb8	en
dc.subject.other	Nonlinear normal modes	en
dc.subject.other	Proper orthogonal (PO) modes	en
dc.subject.other	Computational methods	en
dc.subject.other	Degrees of freedom (mechanics)	en
dc.subject.other	Dynamics	en
dc.subject.other	Galerkin methods	en
dc.subject.other	Hamiltonians	en
dc.subject.other	Nonlinear systems	en
dc.title	A POD-based identification of the reduced dynamics of an exact nonlinear rod loaded transversely	en
heal.type	conferenceItem	en
heal.publicationDate	2003	en
heal.abstract	Reduced dynamics of a nonlinear exact rod is derived by restricting the coupled nonlinear equations of motion onto Proper Orthogonal Modes (POD) identified by a Proper Orthogonal Decomposition of the finite element approximation to the dynamics. For the case of a dominant POD mode, the reduced dynamical system is a geometrically exact nonlinear oscillator. Numerical integration reveals that the phase portrait of the reduced system, for the case of zero dissipation, has Hamiltonian structure. For harmonic forcing at low frequencies, the reduced system predicts exceptionally well the dynamics of the nonlinear rod over a wide range of forcing amplitude. For forcing frequencies in the order of the fundamental frequency for linear bending motions, the reduced model predicts very well the qualitative changes of the dynamics but it underestimates the critical parameters at which the qualitative changes occur at high levels of forcing amplitudes. It is conjectured that the reduced model stemming from the restriction of the full order system onto a single dominant POD describes the dynamics of a nonlinear normal mode of vibration. The POD method can be used to identify the normal modes of vibration of coupled systems with complicated nonlinearities.	en
heal.journalName	Proceedings of the ASME Design Engineering Technical Conference	en
dc.identifier.volume	5 B	en
dc.identifier.spage	1221	en
dc.identifier.epage	1230	en