Vibrations of Bernoulli-Euler beams using the two-phase nonlocal elasticity theory

Fernández-Sáez, José; Zaera, Ramón

Publication:
Vibrations of Bernoulli-Euler beams using the two-phase nonlocal elasticity theory

dc.affiliation.dpto	UC3M. Departamento de Mecánica de Medios Continuos y Teoría de Estructuras	es
dc.affiliation.grupoinv	UC3M. Grupo de Investigación: Dinámica y Fractura de Elementos Estructurales	es
dc.contributor.author	Fernández-Sáez, José
dc.contributor.author	Zaera, Ramón
dc.date.accessioned	2020-12-21T13:05:12Z
dc.date.available	2020-12-21T13:05:12Z
dc.date.issued	2017-10
dc.description.abstract	In this work the problem of the in-plane free vibrations (axial and bending) of a Bernoulli-Euler nanobeam using the mixed local/nonlocal Eringen elasticity theory is studied. The natural frequencies of vibration have been analytically obtained solving two uncoupled integro-differential eigenvalue problems, which are properly transformed in differential eigenvalue problems. Different kinds of end supports have been considered, and the in- fluence of both mixture parameter and length scale has been analysed. The results show the softening effect of the Eringen's nonlocality, which is more pronounced as the local phase fraction decreases. A large number of papers devoted to the dynamics of Bernoulli-Euler beams considering the fully nonlocal Eringen elasticity theory has been previously published. However, as recently stated by Romano, Barretta, Diaco and de Sciarra (2017), the problem is ill-posed in general, and the existence of a solution is an exception, the rule being non-existence. Nevertheless, the presence of a local term in the constitutive equation, leading to the two-phase formulation, renders the problem well-posed. To the best knowledge of the authors, this is the first time an exact solution is presented for a dynamic problem involving structures with constitutive equations corresponding to nonlocal integral Eringen's elasticity.	en
dc.description.sponsorship	The authors are indebted to the Ministerio de Ciencia e Innovación de España (Project DPI-2014-57989-P) for the financial support.	en
dc.format.extent	33
dc.identifier.bibliographicCitation	Fernández-Sáez, J., and Zaera, R. (2017). Vibrations of Bernoulli-Euler beams using the two-phase nonlocal elasticity theory. International Journal of Engineering Science, 119, 232–248	en
dc.identifier.doi	https://doi.org/10.1016/j.ijengsci.2017.06.021
dc.identifier.issn	0020-7225
dc.identifier.publicationfirstpage	232
dc.identifier.publicationlastpage	248
dc.identifier.publicationtitle	International Journal of Engineering Science	en
dc.identifier.publicationvolume	119
dc.identifier.uri	https://hdl.handle.net/10016/31655
dc.identifier.uxxi	AR/0000022280
dc.language.iso	eng
dc.publisher	Elsevier	en
dc.relation.projectID	Gobierno de España. DPI2014-57989-P
dc.rights	© Elsevier, 2017	en
dc.rights	Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.accessRights	open access
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.eciencia	Ingeniería Industrial	es
dc.subject.eciencia	Ingeniería Mecánica	es
dc.subject.other	Mixed Local/Nonlocal Eringen Elasticity Theory	en
dc.subject.other	Dynamic	en
dc.subject.other	Axial Vibrations	en
dc.subject.other	Bending Vibrations	en
dc.subject.other	Nanobeams	en
dc.title	Vibrations of Bernoulli-Euler beams using the two-phase nonlocal elasticity theory	en
dc.type	research article	*
dc.type.hasVersion	AM	*
dspace.entity.type	Publication