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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| Language: | English |
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Wiley
2015-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2015/825342 |
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| author | M. A. De Rosa M. Lippiello H. D. Martin |
| author_facet | M. A. De Rosa M. Lippiello H. D. Martin |
| author_sort | M. A. De Rosa |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-09f573ccfe944dcdb7a7e2a08ac20f81 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-09f573ccfe944dcdb7a7e2a08ac20f812025-08-20T03:55:27ZengWileyThe Scientific World Journal2356-61401537-744X2015-01-01201510.1155/2015/825342825342Free Vibrations of a Cantilevered SWCNT with Distributed Mass in the Presence of Nonlocal EffectM. A. De Rosa0M. Lippiello1H. D. Martin2School of Engineering, University of Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, ItalyDepartment of Structures for Engineering and Architecture, University of Naples “Federico II”, Via Forno Vecchio 36, 80134 Naples, ItalyFacultad Regional Reconquista, UTN, Parque Industrial Reconquista, Reconquista, 3560 Santa Fe, ArgentinaThe 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.http://dx.doi.org/10.1155/2015/825342 |
| spellingShingle | M. A. De Rosa M. Lippiello H. D. Martin Free Vibrations of a Cantilevered SWCNT with Distributed Mass in the Presence of Nonlocal Effect The Scientific World Journal |
| 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 |
| url | http://dx.doi.org/10.1155/2015/825342 |
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