Show simple item record

dc.contributor.authorLewis, Andrew
dc.date.accessioned2020-09-15T00:06:48Z
dc.date.available2020-09-15T00:06:48Z
dc.date.issued2020-11
dc.identifier.citationLewis , A 2020 , ' Approximations to limit cycles for a nonlinear multi-degree-of-freedom system with a cubic nonlinearity through combining the harmonic balance method with perturbation techniques ' , International Journal of Non-Linear Mechanics , vol. 126 , 103590 . https://doi.org/10.1016/j.ijnonlinmec.2020.103590
dc.identifier.issn0020-7462
dc.identifier.otherPURE: 22478099
dc.identifier.otherPURE UUID: 58b34791-7111-4037-b0fb-75124cba78dc
dc.identifier.urihttp://hdl.handle.net/2299/23124
dc.description© 2020 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/.
dc.description.abstractThis paper presents an approach to obtaining higher order approximations to limit cycles of an autonomous multi-degree-of-freedom system with a single cubic nonlinearity based on a first approximation involving first and third harmonics obtained with the harmonic balance method. This first approximation, which is similar to one which has previously been reported in the literature, is an analytical solution, except that the frequency has to be obtained numerically from a polynomial equation of degree 16. An improved solution is then obtained in a perturbation procedure based on the refinement of the harmonic balance solution. The stability of the limit cycles obtained is then investigated using Floquet analysis. The capability of this approach to refine the results obtained by the harmonic balance first approximation is demonstrated, by direct comparison with time domain simulation and frequency components obtained using the Discrete Fourier Transform. The particular case considered was based on an aeroelastic analysis of an all-moving control surface with a nonlinearity in the torsional degree-of-freedom of the root support, and parameters corresponding to air speed, together with linear stiffness and viscous damping of the root support were varied. It is also shown, for the cases considered, how the method can reveal further bifurcational behaviour of the system beyond the initial Hopf bifurcations which first lead to the onset of limit cycle oscillations.en
dc.format.extent13
dc.language.isoeng
dc.relation.ispartofInternational Journal of Non-Linear Mechanics
dc.subjectLimit cycle oscillations; harmonic balance, perturbation methods, Floquet Analysis
dc.subjectEngineering(all)
dc.subjectMathematics(all)
dc.titleApproximations to limit cycles for a nonlinear multi-degree-of-freedom system with a cubic nonlinearity through combining the harmonic balance method with perturbation techniquesen
dc.contributor.institutionCentre for Engineering Research
dc.contributor.institutionMaterials and Structures
dc.contributor.institutionSchool of Physics, Engineering & Computer Science
dc.contributor.institutionDepartment of Engineering and Technology
dc.description.statusPeer reviewed
dc.date.embargoedUntil2021-08-19
rioxxterms.versionAM
rioxxterms.versionofrecordhttps://doi.org/10.1016/j.ijnonlinmec.2020.103590
rioxxterms.typeJournal Article/Review
herts.preservation.rarelyaccessedtrue


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record