A higher order statistical moment based approach for the distribution of eigenvalues of beams with variable cracked depth

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dc.authorid0000-0001-5798-9014en_US
dc.contributor.authorKara, Murat
dc.date.accessioned2023-05-31T11:34:29Z
dc.date.available2023-05-31T11:34:29Z
dc.date.issued2021en_US
dc.departmentBAİBÜ, Mühendislik Fakültesi, Makine Mühendisliği Bölümüen_US
dc.description.abstractStatistical moment analysis proved its accuracy on the determination of mean and variance of free and forced vibration response for the structures having normally distributed global input and output parameters. Apart from the mean and variance, higher order standardized central statistical moments (CSMs) i.e., skewness and kurtosis, must also be evaluated for the nonnormal distributions to obtain probability density function of random variables. In this study, statistical moment analysis is enhanced to calculate higher order CSMs in order to evaluate the distribution of eigenvalues of beams. The method is applied for intact and cracked beams having variable parameters. For the intact beam case, higher order CSMs of eigenvalues are determined corresponding to the normally distributed global variable parameter, i.e., Young's modulus. The latter application of the method is on the cracked beams having a nonnormal variable local parameter, i.e., crack depth. For this case, the method is tested by modelling the crack depth by two different distributions. In this regard, firstly, expressions of CSMs are analytically derived for the mathematical operations (summation and multiplication) of two statistical variables. Then, these expressions are fed to mathematical model (constructed via Rayleigh Ritz method) of cracked beams to calculate statistical moments of eigenvalues. Next, distributions of the eigenvalues corresponding to the variable cracked depth are obtained by utilizing CMSs in Pearson distribution. The results are compared with Monte Carlo simulation and present unique advantages in the sense of computational cost for the structures having variable parameters. (C) 2021 Elsevier Ltd. All rights reserved.en_US
dc.identifier.citationKara, M. (2021). A higher order statistical moment based approach for the distribution of eigenvalues of beams with variable cracked depth. Mechanical Systems and Signal Processing, 161, 107965.en_US
dc.identifier.doi10.1016/j.ymssp.2021.107965
dc.identifier.endpage17en_US
dc.identifier.issn0888-3270
dc.identifier.issn1096-1216
dc.identifier.scopus2-s2.0-85105694497en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage1en_US
dc.identifier.urihttp://dx.doi.org/10.1016/j.ymssp.2021.107965
dc.identifier.urihttps://hdl.handle.net/20.500.12491/11030
dc.identifier.volume161en_US
dc.identifier.wosWOS:000670074900009en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorKara, Murat
dc.language.isoenen_US
dc.publisherAcademic Press Ltd- Elsevier Science Ltden_US
dc.relation.ispartofMechanical Systems and Signal Processingen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectCracked Beamsen_US
dc.subjectStatistical Moment Analysisen_US
dc.subjectPearson Distributionen_US
dc.subjectRayleigh Ritz Methoden_US
dc.subjectHigher Order Momentsen_US
dc.titleA higher order statistical moment based approach for the distribution of eigenvalues of beams with variable cracked depthen_US
dc.typeArticleen_US

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