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Dynamic analysis and non-standard continualization of a Timoshenko beam lattice

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dc.affiliation.dptoUC3M. Departamento de Mecánica de Medios Continuos y Teoría de Estructurases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Dinámica y Fractura de Elementos Estructuraleses
dc.contributor.authorGómez Silva, Francisco
dc.contributor.authorZaera, Ramón
dc.contributor.funderMinisterio de Ciencia e Innovación (España)es
dc.contributor.funderAgencia Estatal de Investigación (España)es
dc.date.accessioned2023-09-28T09:33:16Z
dc.date.available2023-09-28T09:33:16Z
dc.date.issued2022-01-15
dc.description.abstractIn this paper, a Timoshenko beam lattice, made up of a chain of masses and straight segments, is proposed, considering bending and shear deformation by means of linear rotational and transverse springs, respectively. Different standard and non-standard continualization methods are applied to it, highlighting here for the first time the suitability of taking the coupled discrete governing equations as a starting point for deriving new continuum models. Several novel low order non-classical continuum models are obtained, with the aim of reliably capturing size-effects and reflecting the dispersive behaviour of the discrete system. Low order governing equations prevents the need for extra boundary conditions when finite (bounded) solids are treated. An extensive analysis of the transition frequency, which initiates the shear propagation spectrum, has been carried out, examining its influence for the discrete and non-standard continuum models. The natural frequencies of a finite solid with two different boundary conditions are obtained through an edge treatment applied here for the first time to this kind of lattices, thus making it possible to solve the clamped-free edges configuration. The reliability of these approaches is evaluated by comparing their dynamic behaviours with that of the discrete system (taken as a reference), through both dispersion and vibration analyses, some of the new proposed continuum models successfully capturing the behaviour of the discrete one, even for high wavenumbers. Moreover, the appearance of physical inconsistencies is examined.en
dc.description.sponsorshipThe authors acknowledge support from MCIN/ AEI /10.13039/501100011033 under Grants numbers PGC2018-098218-B-I00 and PRE2019-088002. FEDER: A way to make Europe. ESF invests in your future.en
dc.format.extent18
dc.identifier.bibliographicCitationGómez-Silva, F., & Zaera, R. (2022). Dynamic analysis and non-standard continualization of a Timoshenko beam lattice. International Journal of Mechanical Sciences, 214, 106873.en
dc.identifier.doihttps://doi.org/10.1016/j.ijmecsci.2021.106873
dc.identifier.issn0020-7403
dc.identifier.publicationfirstpage1
dc.identifier.publicationissue106873
dc.identifier.publicationlastpage18
dc.identifier.publicationtitleInternational Journal of Mechanical Sciencesen
dc.identifier.publicationvolume214
dc.identifier.urihttps://hdl.handle.net/10016/38464
dc.identifier.uxxiAR/0000031185
dc.language.isoengen
dc.publisherElsevieren
dc.relation.projectIDGobierno de España. PGC2018-098218-B-I00es
dc.relation.projectIDGobierno de España. PRE2019-088002es
dc.relation.projectIDAT-2022
dc.rights© 2022 The Authors.en
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaIngeniería Mecánicaes
dc.subject.ecienciaMaterialeses
dc.subject.otherContinualizationen
dc.subject.otherDispersive Behaviouren
dc.subject.otherNatural Frequenciesen
dc.subject.otherPseudo-Differential Operatoren
dc.subject.otherTimoshenko Beam Latticeen
dc.subject.otherTransition Frequencyen
dc.titleDynamic analysis and non-standard continualization of a Timoshenko beam latticeen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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