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dc.contributor.authorLewis, Andrew
dc.date.accessioned2019-03-26T15:10:22Z
dc.date.available2019-03-26T15:10:22Z
dc.date.issued2019-04-01
dc.identifier.citationLewis , A 2019 , ' Refined Analytical Approximations to Limit Cycles for Non-Linear Multi-Degree-of-Freedom Systems ' , International Journal of Non-Linear Mechanics , vol. 110 , NLM_3132 , pp. 58-68 . https://doi.org/10.1016/j.ijnonlinmec.2018.12.009
dc.identifier.issn0020-7462
dc.identifier.otherPURE: 16084492
dc.identifier.otherPURE UUID: 6c8de3ef-cd89-474c-957b-208083b45db8
dc.identifier.otherScopus: 85060437509
dc.identifier.urihttp://hdl.handle.net/2299/21221
dc.description.abstractThis paper presents analytical higher order approximations to limit cycles of an autonomous multi-degree-of-freedom system based on an integro-differential equation method for obtaining periodic solutions to nonlinear differential equations. The stability of the limit cycles obtained was then investigated using a method for carrying out Floquet analysis based on developments to extensions of the method for solving Hill's Determinant arising in analysing the Mathieu equation, which have previously been reported in the literature. The results of the Floquet analysis, together with the limit cycle predictions, have then been used to provide some estimates of points on the boundary of the domain of attraction of stable equilibrium points arising from a sub-critical Hopf bifurcation. This was achieved by producing a local approximation to the stable manifold of the unstable limit cycle that occurs. The integro-differential equation to be solved for the limit cycles involves no approximations. These only arise through the iterative approach adopted for its solution in which the first approximation is that which would be obtained from the harmonic balance method using only fundamental frequency terms. The higher order approximations are shown to give significantly improved predictions for the limit cycles for the cases considered. The Floquet analysis based approach to predicting the boundary of domains of attraction met with some success for conditions just following a sub-critical Hopf bifurcation. Although this study has focussed on cubic non-linearities, the method presented here could equally be used to refine limit cycle predictions for other non-linearity types.en
dc.format.extent11
dc.language.isoeng
dc.relation.ispartofInternational Journal of Non-Linear Mechanics
dc.rightsEmbargoed
dc.subjectFloquet analysis
dc.subjectLimit cycle oscillations
dc.subjectStability domains
dc.subjectMechanics of Materials
dc.subjectMechanical Engineering
dc.subjectApplied Mathematics
dc.titleRefined Analytical Approximations to Limit Cycles for Non-Linear Multi-Degree-of-Freedom Systemsen
dc.contributor.institutionSchool of Engineering and Technology
dc.contributor.institutionCentre for Engineering Research
dc.contributor.institutionMaterials and Structures
dc.description.statusPeer reviewed
dc.date.embargoedUntil2020-01-25
dc.identifier.urlhttp://www.scopus.com/inward/record.url?scp=85060437509&partnerID=8YFLogxK
dc.relation.schoolSchool of Engineering and Technology
dc.description.versiontypeFinal Accepted Version
dcterms.dateAccepted2019-04-01
rioxxterms.versionAM
rioxxterms.versionofrecordhttps://doi.org/10.1016/j.ijnonlinmec.2018.12.009
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
rioxxterms.licenseref.startdate2020-01-25
rioxxterms.typeJournal Article/Review
herts.preservation.rarelyaccessedtrue
herts.date.embargo2020-01-25
herts.rights.accesstypeEmbargoed


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