One-dimensional dispersion phenomena in terms of fractional media

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dc.contributor.author Sumelka, Wojciech
dc.contributor.author Zaera, Ramón
dc.contributor.author Fernández-Sáez, José
dc.date.accessioned 2023-01-17T10:59:58Z
dc.date.available 2023-01-17T10:59:58Z
dc.date.issued 2016-09-19
dc.identifier.bibliographicCitation Sumelka, W., Zaera, R., & Fernández-Sáez, J. (2016). One-dimensional dispersion phenomena in terms of fractional media. European Physical Journal Plus, 131(9)
dc.identifier.issn 2190-5444
dc.identifier.uri http://hdl.handle.net/10016/36282
dc.description.abstract It is well know that structured solids present dispersive behaviour which cannot be captured by the classical continuum mechanics theories. A canonical problem in which this can be seen is the wave propagation in the Born-Von Karman lattice. In this paper the dispersive effects in a 1D structured solid is analysed using the Fractional Continuum Mechanics (FCM) approach previously proposed by Sumelka (2013). The formulation uses the Riesz-Caputo (RC) fractional derivative and introduces two phenomenological/material parameters: 1) the size of non-local surrounding l(f), which plays the role of the lattice spacing; and 2) the order of fractional continua a, which can be devised as a fitting parameter. The results obtained with this approach have been compared with the reference dispersion curve of Born-Von Karman lattice, and the capability of the fractional model to capture the size effects present in the dynamic behaviour of discrete systems has been proved.
dc.description.sponsorship The authors wish to acknowledge the Ministerio de Economía y Competitividad de España for the financial support, under grant number DPI2014-57989-P.
dc.format.extent 9
dc.language.iso eng
dc.publisher Springer
dc.rights © The Author(s) 2016. This article is published with open access at Springerlink.com
dc.rights This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
dc.rights Atribución 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by/3.0/es/
dc.subject.other Couple stress theory
dc.subject.other Continuum-mechanics
dc.subject.other Nonlocal elasticity
dc.subject.other Calculus
dc.subject.other Derivatives
dc.subject.other Models
dc.subject.other Beams
dc.title One-dimensional dispersion phenomena in terms of fractional media
dc.type article
dc.subject.eciencia Ingeniería Mecánica
dc.subject.eciencia Materiales
dc.identifier.doi https://doi.org/10.1140/epjp/i2016-16320-3
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. DPI2014-57989-P
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 1
dc.identifier.publicationissue 9
dc.identifier.publicationlastpage 9
dc.identifier.publicationtitle The European Physical Journal Plus
dc.identifier.publicationvolume 131
dc.identifier.uxxi AR/0000018290
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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