Exact solution of the Mindlin–Herrmann model for longitudinal vibration of an isotropic rod

dc.contributor.authorTenkam, H.M.
dc.contributor.authorAnguelov, Roumen
dc.contributor.authorFedotov, I.
dc.contributor.authorShatalov, M.
dc.contributor.emailmichel.djouosseu@up.ac.zaen_ZA
dc.date.accessioned2015-11-26T07:18:01Z
dc.date.issued2016-08
dc.description.abstractThis paper presents a new approach to the problem of coupled longitudinal and transversal propagation of stress waves in an isotropic thick and elastic rod, based on the Mindlin-Herrmann theory. The novelty is that, the Hamilton vriational principle is used not only for derivation of the governing equations and set of natural boundary conditions, but also for obtaining the exact solution in terms Green functions directly from the Langrangian. The success of this approach is based on the existence of multiple orthogonalities of the eigenfuctions. The proposed method is much easier than the standard approach of building Green functions. A numerical example illustrates the method of finding eigenfrequencies and eigenfunctions for isotropic Mindlin-Herrmann rod.en_ZA
dc.description.embargo2017-08-30
dc.description.librarianhb2015en_ZA
dc.description.sponsorshipNational Research Foundation (NRF) of South Africa (Grant No: 85177)en_ZA
dc.description.urihttp://link.springer.com/journal/10665en_ZA
dc.identifier.citationTenkam, HM, Anguelov, R, Fedotov, I & Shatalov, M 2016, 'Exact solution of the Mindlin–Herrmann model for longitudinal vibration of an isotropic rod', Journal of Engineering Mathematics, vol. 99, no. 1, pp. 185-201.en_ZA
dc.identifier.issn0022-0833 (print)
dc.identifier.issn1573-2703 (online)
dc.identifier.other10.1007/s10665-015-9827-5
dc.identifier.urihttp://hdl.handle.net/2263/50923
dc.language.isoenen_ZA
dc.publisherSpringeren_ZA
dc.rights© Springer Science+Business Media Dordrecht 2015. The original publication is available at : http://link.springer.com/journal/10665.en_ZA
dc.subjectEigenfunction orthogonalitiesen_ZA
dc.subjectGreen functionen_ZA
dc.subjectLongitudinal-transversal vibrationen_ZA
dc.subjectMindlin-Herrmann modelen_ZA
dc.subjectSelf-adjoint operatoren_ZA
dc.titleExact solution of the Mindlin–Herrmann model for longitudinal vibration of an isotropic roden_ZA
dc.typePostprint Articleen_ZA

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