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Free Vibrations of a Cantilevered SWCNT with Distributed Mass in the Presence of Nonlocal Effect

The Hamilton principle is applied to deduce the free vibration frequencies of a cantilever single-walled carbon nanotube (SWCNT) in the presence of an added mass, which can be distributed along an arbitrary part of the span. The nonlocal elasticity theory by Eringen has been employed, in order to ta...

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Detalles Bibliográficos
Autores principales: De Rosa, M. A., Lippiello, M., Martin, H. D.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4359880/
https://www.ncbi.nlm.nih.gov/pubmed/25815371
http://dx.doi.org/10.1155/2015/825342
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author De Rosa, M. A.
Lippiello, M.
Martin, H. D.
author_facet De Rosa, M. A.
Lippiello, M.
Martin, H. D.
author_sort De Rosa, M. A.
collection PubMed
description The Hamilton principle is applied to deduce the free vibration frequencies of a cantilever single-walled carbon nanotube (SWCNT) in the presence of an added mass, which can be distributed along an arbitrary part of the span. The nonlocal elasticity theory by Eringen has been employed, in order to take into account the nanoscale effects. An exact formulation leads to the equations of motion, which can be solved to give the frequencies and the corresponding vibration modes. Moreover, two approximate semianalytical methods are also illustrated, which can provide quick parametric relationships. From a more practical point of view, the problem of detecting the mass of the attached particle has been solved by calculating the relative frequency shift due to the presence of the added mass: from it, the mass value can be easily deduced. The paper ends with some numerical examples, in which the nonlocal effects are thoroughly investigated.
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spelling pubmed-43598802015-03-26 Free Vibrations of a Cantilevered SWCNT with Distributed Mass in the Presence of Nonlocal Effect De Rosa, M. A. Lippiello, M. Martin, H. D. ScientificWorldJournal Research Article The Hamilton principle is applied to deduce the free vibration frequencies of a cantilever single-walled carbon nanotube (SWCNT) in the presence of an added mass, which can be distributed along an arbitrary part of the span. The nonlocal elasticity theory by Eringen has been employed, in order to take into account the nanoscale effects. An exact formulation leads to the equations of motion, which can be solved to give the frequencies and the corresponding vibration modes. Moreover, two approximate semianalytical methods are also illustrated, which can provide quick parametric relationships. From a more practical point of view, the problem of detecting the mass of the attached particle has been solved by calculating the relative frequency shift due to the presence of the added mass: from it, the mass value can be easily deduced. The paper ends with some numerical examples, in which the nonlocal effects are thoroughly investigated. Hindawi Publishing Corporation 2015 2015-03-01 /pmc/articles/PMC4359880/ /pubmed/25815371 http://dx.doi.org/10.1155/2015/825342 Text en Copyright © 2015 M. A. De Rosa et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
De Rosa, M. A.
Lippiello, M.
Martin, H. D.
Free Vibrations of a Cantilevered SWCNT with Distributed Mass in the Presence of Nonlocal Effect
title Free Vibrations of a Cantilevered SWCNT with Distributed Mass in the Presence of Nonlocal Effect
title_full Free Vibrations of a Cantilevered SWCNT with Distributed Mass in the Presence of Nonlocal Effect
title_fullStr Free Vibrations of a Cantilevered SWCNT with Distributed Mass in the Presence of Nonlocal Effect
title_full_unstemmed Free Vibrations of a Cantilevered SWCNT with Distributed Mass in the Presence of Nonlocal Effect
title_short Free Vibrations of a Cantilevered SWCNT with Distributed Mass in the Presence of Nonlocal Effect
title_sort free vibrations of a cantilevered swcnt with distributed mass in the presence of nonlocal effect
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4359880/
https://www.ncbi.nlm.nih.gov/pubmed/25815371
http://dx.doi.org/10.1155/2015/825342
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