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dc.contributor.authorHawes, Daviden
dc.contributor.authorLangley, Robinen
dc.date.accessioned2015-09-03T12:51:29Z
dc.date.available2015-09-03T12:51:29Z
dc.date.issued2015-10-06en
dc.identifier.citationHawes & Langley. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science (2015) Vol. 230, Issue 6, pp. 888-899. doi: 10.1177/0954406215607544en
dc.identifier.issn0954-4062
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/250478
dc.description.abstractWhen compared to independent harmonic or stochastic excitation, there exist relatively few methods to model the response of nonlinear systems to a combination of deterministic and stochastic vibration despite the likelihood of harmonic oscillations containing noise in realistic applications. This paper uses the Duffing oscillator to illustrate how the joint probability density function (JPDF) of the displacement and velocity responds to this form of excitation. Monte Carlo simulations were performed to generate the JPDF which was observed to spread around the attractor that would be seen if only deterministic excitation was present. This paper assesses the ability of a useful class of methods, global weighted residual methods, to produce the geometrically complex JPDF responses produced from harmonic and white noise excitation. A technique using a JPDF in the form of a Gram-Charlier type C series was found to produce accurate results, although the method fails due to ill-conditioning as the shape of the JPDF required by the dynamics becomes too complex.
dc.description.sponsorshipThe authors would like to thank the EPSRC Doctoral Training Award for funding this research.
dc.languageEnglishen
dc.language.isoenen
dc.publisherSAGE
dc.rightsAttribution-NonCommercial 2.0 UK: England & Wales*
dc.rights.urihttp://creativecommons.org/licenses/by-nc/2.0/uk/*
dc.subjectnonlinearen
dc.subjectstochasticen
dc.subjectdeterministicen
dc.subjectvibrationen
dc.subjectduffingen
dc.titleNumerical methods for calculating the response of a deterministic and stochastically excited Duffing oscillatoren
dc.typeArticle
dc.description.versionThis is the author accepted manuscript. The final version is available from SAGE via http://dx.doi.org/10.1177/0954406215607544en
prism.endingPage899
prism.publicationDate2015en
prism.publicationNameProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Scienceen
prism.startingPage888
prism.volume230en
dc.rioxxterms.funderEPSRC
rioxxterms.versionofrecord10.1177/0954406215607544en
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2015-10-06en
dc.contributor.orcidHawes, David [0000-0002-6203-0067]
dc.contributor.orcidLangley, Robin [0000-0001-9978-9790]
dc.identifier.eissn2041-2983
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEPSRC (1355112)
pubs.funder-project-idEPSRC (EP/L504920/1)


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Attribution-NonCommercial 2.0 UK: England & Wales
Except where otherwise noted, this item's licence is described as Attribution-NonCommercial 2.0 UK: England & Wales