On the detection of artifacts in Harmonic Balance solutions of nonlinear oscillators

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dc.contributor.authorWagner, Utz von
dc.contributor.authorLentz, Lukas
dc.date.accessioned2020-03-19T14:23:44Z
dc.date.available2020-03-19T14:23:44Z
dc.date.issued2018-09-06
dc.description.abstractHarmonic Balance is a very popular semi-analytic method in nonlinear dynamics. It is easy to apply and is known to produce good results for numerous examples. Adding an error criterion taking into account the neglected terms allows an evaluation of the results. Looking on the therefore determined error for increasing ansatz orders, it can be evaluated whether a solution really exists or is an artifact. For the low-error solutions additionally a stability analysis is performed which allows the classification of the solutions in three types, namely in large error solutions, low error stable solutions and low error unstable solution. Examples considered in this paper are the classical Duffing oscillator and an extended Duffing oscillator with nonlinear damping and excitation. Compared to numerical integration, the proposed procedure offers a faster calculation of existing multiple solutions and their character.en
dc.identifier.eissn1872-8480
dc.identifier.issn0307-904X
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/10942
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-9832
dc.language.isoenen
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subject.ddc510 Mathematikde
dc.subject.othernonlinear dynamicsen
dc.subject.otherharmonic balance methoden
dc.subject.otherDuffing oscillatoren
dc.titleOn the detection of artifacts in Harmonic Balance solutions of nonlinear oscillatorsen
dc.typeArticleen
dc.type.versionacceptedVersionen
dcterms.bibliographicCitation.doi10.1016/j.apm.2018.08.013en
dcterms.bibliographicCitation.journaltitleApplied Mathematical Modellingen
dcterms.bibliographicCitation.originalpublishernameElsevieren
dcterms.bibliographicCitation.originalpublisherplaceAmsterdam [u.a.]en
dcterms.bibliographicCitation.pageend414en
dcterms.bibliographicCitation.pagestart408en
dcterms.bibliographicCitation.volume65en
tub.accessrights.dnbfree*
tub.affiliationFak. 5 Verkehrs- und Maschinensysteme::Inst. Mechanik::FG Mechatronische Maschinendynamikde
tub.affiliation.facultyFak. 5 Verkehrs- und Maschinensystemede
tub.affiliation.groupFG Mechatronische Maschinendynamikde
tub.affiliation.instituteInst. Mechanikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen

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