Discrete singular convolution–polynomial chaos expansion method for free vibration analysis of non-uniform uncertain beams

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dc.authorid0000-0001-5798-9014
dc.authorid0000-0002-1896-7629
dc.authorid0000-0001-5955-7477
dc.contributor.authorSeçgin, Abdullah
dc.contributor.authorKara, Murat
dc.contributor.authorFerguson, Neil
dc.date.accessioned2021-06-23T18:57:13Z
dc.date.available2021-06-23T18:57:13Z
dc.date.issued2021
dc.departmentBAİBÜ, Mühendislik Fakültesi, Makine Mühendisliği Bölümüen_US
dc.description.abstractThis article enhances the discrete singular convolution method for free vibration analysis of non-uniform thin beams with variability in their geometrical and material properties such as thickness, specific volume (inverse of density) and Young’s modulus. The discrete singular convolution method solves the differential equation of motion of a structure with a high accuracy using a small number of discretisation points. The method uses polynomial chaos expansion to express these variabilities simulating uncertainty in a closed form. Non-uniformity is locally provided by changing the cross section and Young’s modulus of the beam along its length. In this context, firstly natural frequencies of deterministic uniform and non-uniform beams are predicted via the discrete singular convolution. These results are compared with finite element calculations and analytical solutions (if available) for the purpose of verification. Next, the uncertainty of the beam because of geometrical and material variabilities is modelled in a global manner by polynomial chaos expansion to predict probability distribution functions of the natural frequencies. Monte Carlo simulations are then performed for validation purpose. Results show that the proposed algorithm of the discrete singular convolution with polynomial chaos expansion is very accurate and also efficient, regarding computation cost, in handling non-uniform beams having material and geometrical variabilities. Therefore, it promises that it can be reliably applied to more complex structures having uncertain parameters.en_US
dc.description.sponsorshipTürkiye Bilimsel ve Teknolojik Araştirma Kurumu, TÜBITAKen_US
dc.description.sponsorshipThe author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study is supported by “The Scientific and Technological Research Council of Turkey, TUBITAK” in the frame of TUBITAK 2219 programme.en_US
dc.identifier.doi10.1177/1077546320988190
dc.identifier.issn1077-5463
dc.identifier.scopus2-s2.0-85101047931en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.1177/1077546320988190
dc.identifier.urihttps://hdl.handle.net/20.500.12491/5152
dc.identifier.wosWOS:000682988400001en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorKara, Murat
dc.language.isoenen_US
dc.publisherSAGE Publications Inc.en_US
dc.relation.ispartofJVC/Journal of Vibration and Controlen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectDiscrete Singular Convolutionen_US
dc.subjectNon-uniform Beamen_US
dc.subjectPolynomial Chaos Expansionen_US
dc.subjectUncertaintyen_US
dc.titleDiscrete singular convolution–polynomial chaos expansion method for free vibration analysis of non-uniform uncertain beamsen_US
dc.typeArticleen_US

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