Statics and dynamics of nanorods embedded in an elastic medium: Nonlocal elasticity and lattice formulations

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dc.authorwosidAydogdu, Metin/A-2596-2009
dc.contributor.authorChallamel, Noel
dc.contributor.authorAydogdu, Metin
dc.contributor.authorElishakoff, Isaac
dc.date.accessioned2024-06-12T11:09:18Z
dc.date.available2024-06-12T11:09:18Z
dc.date.issued2018
dc.departmentTrakya Üniversitesien_US
dc.description.abstractThis paper is focused on the static and the dynamic behaviour of an axial lattice (with direct neighbouring interaction) loaded by some distributed forces and in interaction with an elastic medium. Some exact analytical solutions are provided both in static and in dynamic settings, for the finite lattice system under general boundary conditions including fixed- and free-end boundary conditions. A nonlocal rod model based on the introduction of one additional length scale, is then constructed by continualization scheme of the lattice difference equations, to capture the scale effects associated with the lattice spacing. The continualized nonlocal model coincides with a phenomenological Eringen's nonlocal model, except eventually for the boundary conditions. These new continualized nonlocal boundary conditions are derived from the end lattice boundary conditions. The enriched nonlocal wave equation augmented by the elastic medium interaction has a spatial derivative which coincides with the local wave equation, thus avoiding the need of higher-order boundary conditions. The static and the dynamic responses of the equivalent nonlocal bar are also analytically studied and compared to the lattice problem. It is shown that the nonlocal solution efficiently fits the lattice one, both in static and in dynamic settings. The nonlocal model can be also introduced from variational arguments, thus leading to a nonlocal optimal Rayleigh quotient. For very high frequencies, the nonlocal model is corrected by a two-length scale model, which is shown to capture efficiently the frequency spectra of the lattice model for all frequency range. (C) 2017 Elsevier Masson SAS. All rights reserved.en_US
dc.identifier.doi10.1016/j.euromechsol.2017.09.009
dc.identifier.endpage271en_US
dc.identifier.issn0997-7538
dc.identifier.issn1873-7285
dc.identifier.scopus2-s2.0-85031996782en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage254en_US
dc.identifier.urihttps://doi.org/10.1016/j.euromechsol.2017.09.009
dc.identifier.urihttps://hdl.handle.net/20.500.14551/22764
dc.identifier.volume67en_US
dc.identifier.wosWOS:000418967700020en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevier Science Bven_US
dc.relation.ispartofEuropean Journal Of Mechanics A-Solidsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectNonlocal Elasticityen_US
dc.subjectLattice Modelsen_US
dc.subjectStaticsen_US
dc.subjectDynamicsen_US
dc.subjectMicrostructured Roden_US
dc.subjectInteraction With Elastic Mediumen_US
dc.subjectDistributed Forcesen_US
dc.subjectLongitudinal-Wave Propagationen_US
dc.subjectContinuum Modelsen_US
dc.subjectEquationsen_US
dc.subjectRepresentationen_US
dc.subjectDerivationen_US
dc.subjectVibrationen_US
dc.subjectNanotubesen_US
dc.subjectMechanicsen_US
dc.subjectSystemsen_US
dc.subjectChainsen_US
dc.titleStatics and dynamics of nanorods embedded in an elastic medium: Nonlocal elasticity and lattice formulationsen_US
dc.typeArticleen_US

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