Analysis of time-periodic systems when corresponding equations do not contain a small parameter explicitly

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dc.contributor.author Sorokin, Vladislav en
dc.contributor.editor Dimitrovová, Z en
dc.contributor.editor de Almeida, JR en
dc.contributor.editor Gonçalves, R en
dc.coverage.spatial Lisbon, Portugal en
dc.date.accessioned 2017-08-01T00:27:45Z en
dc.date.issued 2013 en
dc.identifier.citation International Conference on Vibration Problems, Lisbon, Portugal, 09 Sep 2013 - 12 Sep 2013. Editors: Dimitrovová Z, de Almeida JR, Gonçalves R . Proceedings of the 11th International Conference on Vibration Problems (ICOVP 2013). 10 pages. 2013 en
dc.identifier.isbn 978-989-96264-4-7 en
dc.identifier.uri http://hdl.handle.net/2292/34647 en
dc.description.abstract There are many approaches to study equations with time-periodic coefficients, in which a small parameter may be assigned, in particular the classical asymptotic methods. The present paper is concerned with the analysis of the applicability of these approaches for solving nonlinear equations, which don’t contain a small parameter explicitly. A new modifi-cation of the method of direct separation of motions (MDSM) [1,2], which may be employed to study such equations, is proposed. As an example a classical problem about the stability of a pendulum with vibrating suspension axis is considered in an unconventional case, when the frequency of external loading and the natural frequency of the pendulum in the absence of this loading are of the same order. As the result it is shown that in the considered range of parameters not only the effective “stiffness” of the system changes due to the external loading, but also its effective “mass”. It is noted that application of the classical asymptotic methods in this case leads to erroneous results. A correlation between the proposed modification of the MDSM and Ritz’s method of harmon-ic balance, Van der Pol’s method of slowly varying amplitudes, the classical asymptotic methods and other approaches is discussed. en
dc.description.uri http://www.icoev.org/index.php/icovp-2013/proceedings en
dc.relation.ispartof International Conference on Vibration Problems en
dc.relation.ispartofseries Proceedings of the 11th International Conference on Vibration Problems (ICOVP 2013) en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.title Analysis of time-periodic systems when corresponding equations do not contain a small parameter explicitly en
dc.type Conference Item en
pubs.author-url http://www.icoev.org/components/com_breezingforms/exports/294_0.pdf en
pubs.finish-date 2013-09-12 en
pubs.start-date 2013-09-09 en
dc.rights.accessrights http://purl.org/eprint/accessRights/RestrictedAccess en
pubs.subtype Proceedings en
pubs.elements-id 625416 en
pubs.org-id Engineering en
pubs.org-id Mechanical Engineering en
pubs.record-created-at-source-date 2017-05-12 en


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