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The Scientific World Journal
Volume 2015, Article ID 825342, 12 pages
Research Article

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

1School of Engineering, University of Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy
2Department of Structures for Engineering and Architecture, University of Naples “Federico II”, Via Forno Vecchio 36, 80134 Naples, Italy
3Facultad Regional Reconquista, UTN, Parque Industrial Reconquista, Reconquista, 3560 Santa Fe, Argentina

Received 7 October 2014; Accepted 19 December 2014

Academic Editor: Sayan Bhattacharyya

Copyright © 2015 M. A. De Rosa et al. 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.


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.