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An engineering perspective on the numerics of quasi-periodic oscillations

dc.date.accessioned2022-08-16T09:39:29Z
dc.date.available2022-08-16T09:39:29Z
dc.date.issued2022-04-29
dc.identifierdoi:10.17170/kobra-202206016279
dc.identifier.urihttp://hdl.handle.net/123456789/14059
dc.description.sponsorshipGefördert im Rahmen des Projekts DEALger
dc.language.isoeng
dc.rightsNamensnennung 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectquasi-periodic motioneng
dc.subjectinvariant manifoldseng
dc.subjectgeneralized invariance equationeng
dc.subjecthyper-time methodseng
dc.subjectmulti-dimensional Fourier-Galerkin methodeng
dc.subjectfinite difference methodeng
dc.subjectcomparison of methodseng
dc.subjectmulti-harmonic balance methodeng
dc.subject.ddc620
dc.titleAn engineering perspective on the numerics of quasi-periodic oscillationseng
dc.typeAufsatz
dcterms.abstractThe phenomenon of quasi-periodicity in deterministic dynamical systems describes stationary solutions, which neither exhibit a finite period length nor are chaotic. Recently, an increasing demand for robust numerical methods is driven by applied dynamics and industrial applications. In this context, direct time integration proves to be impractical due to extensive integration intervals. Therefore, in a first step, this contribution aims on giving an application oriented survey of the basic theory as well as alternative concepts. In the following, the focus is set on the direct computation of invariant manifolds (surfaces) on which quasi-periodic solutions evolve. This approach offers a unique framework from which classical methods (e.g., the multi-harmonic-balance) can be systematically deduced and mutual similarities between different methods may be revealed. This contribution starts with a brief summary of related mathematical basics, which is followed by an overview of available methods. Subsequently, the computation of invariant manifolds by means of solving a partial differential equation is emphasized. These PDEs may be formulated using different parametrization strategies. Here, the concept of hyper-time parametrization is particularly interesting, since it is a promising starting point for the development of numerical schemes with general applicability in engineering problems. In order to solve the underlying PDE, various methods may be used. The implementation of a Fourier-Galerkin method as well as a finite difference method is presented and compared on the basis of computational results of the van-der-Pol equation (with and without forcing). Moreover, it is demonstrated that both methods apply to periodic as well as quasi-periodic solutions alike. In order to exemplify the practical use, these methods are applied to a generic rotordynamic model problem.eng
dcterms.accessRightsopen access
dcterms.creatorBäuerle, Simon
dcterms.creatorFiedler, Robert
dcterms.creatorHetzler, Hartmut
dc.relation.doidoi:10.1007/s11071-022-07407-5
dc.subject.swdParametrisierungger
dc.subject.swdEndliche Mathematikger
dc.subject.swdFinite-Differenzen-Methodeger
dc.subject.swdDifferentialgleichungger
dc.title.subtitleA comparison of two hyper-time approaches based on a unified frameworkeng
dc.type.versionpublishedVersion
dcterms.source.identifiereissn:1573-269X
dcterms.source.issueIssue 4
dcterms.source.journalNonlinear Dynamicseng
dcterms.source.pageinfo3927-3950
dcterms.source.volumeVolume 108
kup.iskupfalse


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