Advanced proper orthogonal decomposition tools: Using reduced order models to identify normal modes of vibration and slow invariant manifolds in the dynamics of planar nonlinear rods

Georgiou, I

dc.contributor.author	Georgiou, I	en
dc.date.accessioned	2014-03-01T01:21:48Z
dc.date.available	2014-03-01T01:21:48Z
dc.date.issued	2005	en
dc.identifier.issn	0924-090X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16376
dc.subject	Coupled vibrations	en
dc.subject	Geometric singular perturbations	en
dc.subject	Normal modes of vibration	en
dc.subject	Proper orthogonal decomposition	en
dc.subject	Reduced order system	en
dc.subject	Slow invariant manifolds	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Equations of motion	en
dc.subject.other	Finite element method	en
dc.subject.other	Natural frequencies	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Nonlinear systems	en
dc.subject.other	Perturbation techniques	en
dc.subject.other	Vibrations (mechanical)	en
dc.subject.other	Coupled vibrations	en
dc.subject.other	Geometeric singular perturbations	en
dc.subject.other	Normal modes of vibration	en
dc.subject.other	Proper orthogonal decompomposition	en
dc.subject.other	Reduced order system	en
dc.subject.other	Slow invariant manifolds	en
dc.subject.other	Structural analysis	en
dc.title	Advanced proper orthogonal decomposition tools: Using reduced order models to identify normal modes of vibration and slow invariant manifolds in the dynamics of planar nonlinear rods	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s11071-005-2793-0	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s11071-005-2793-0	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	Reduced order models for the dynamics of geometrically exact planar rods are derived by projecting the nonlinear equations of motion onto a subspace spanned by a set of proper orthogonal modes. These optimal modes are identified by a proper orthogonal decomposition processing of high-resolution finite element dynamics. A three-degree-of-freedom reduced system is derived to study distinct categories of motions dominated by a single POD mode. The modal analysis of the reduced system characterizes in a unique fashion for these motions, since its linear natural frequencies are near to the natural frequencies of the full-order system. For free motions characterized by a single POD mode, the eigen-vector matrix of the derived reduced system coincides with the principal POD-directions. This property reflects the existence of a normal mode of vibration, which appears to be close to a slow invariant manifold. Its shape is captured by that of the dominant POD mode. The modal analysis of the POD-based reduced order system provides a potentially valuable tool to characterize the spatio-temporal complexity of the dynamics in order to elucidate connections between proper orthogonal modes and nonlinear normal modes of vibration. © Springer 2005.	en
heal.publisher	SPRINGER	en
heal.journalName	Nonlinear Dynamics	en
dc.identifier.doi	10.1007/s11071-005-2793-0	en
dc.identifier.isi	ISI:000230267900004	en
dc.identifier.volume	41	en
dc.identifier.issue	1-3	en
dc.identifier.spage	69	en
dc.identifier.epage	110	en