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Technologies 2015, 3(4), 259-284; doi:10.3390/technologies3040259

Refined 2D and Exact 3D Shell Models for the Free Vibration Analysis of Single- and Double-Walled Carbon Nanotubes

1
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, corso Duca degli Abruzzi 24, Torino 10129, Italy
2
Department of Civil, Chemical, Enviromental and Material Engineering, Alma Mater Studiorum, University of Bologna, viale Risorgimento 2, Bologna 40136, Italy
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editors: Luciano Feo and Raimondo Luciano
Received: 21 August 2015 / Revised: 20 November 2015 / Accepted: 25 November 2015 / Published: 4 December 2015
(This article belongs to the Special Issue Nanotechnology in Construction)
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Abstract

The present paper talks about the free vibration analysis of simply supported Single- and Double-Walled Carbon Nanotubes (SWCNTs and DWCNTs). Refined 2D Generalized Differential Quadrature (GDQ) shell methods and an exact 3D shell model are compared. A continuum approach (based on an elastic three-dimensional shell model) is used for natural frequency investigation of SWCNTs and DWCNTs. SWCNTs are defined as isotropic cylinders with an equivalent thickness and Young modulus. DWCNTs are defined as two concentric isotropic cylinders (with an equivalent thickness and Young modulus) which can be linked by means of the interlaminar continuity conditions or by means of van der Waals interactions. Layer wise approaches are mandatory for the analysis of van der Waals forces in DWCNTs. The effect of van der Waals interaction between the two cylinders is shown for different DWCNT lengths, diameters and vibration modes. The accuracy of beam models and classical 2D shell models in the free vibration analysis of SWCNTs and DWCNTs is also investigated. View Full-Text
Keywords: single-walled carbon nanotube; double-walled carbon nanotube; free vibrations; van der Waals interaction; three-dimensional shell model; exact solution; two-dimensional shell models; generalized differential quadrature method single-walled carbon nanotube; double-walled carbon nanotube; free vibrations; van der Waals interaction; three-dimensional shell model; exact solution; two-dimensional shell models; generalized differential quadrature method
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. (CC BY 4.0).

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MDPI and ACS Style

Brischetto, S.; Tornabene, F.; Fantuzzi, N.; Bacciocchi, M. Refined 2D and Exact 3D Shell Models for the Free Vibration Analysis of Single- and Double-Walled Carbon Nanotubes. Technologies 2015, 3, 259-284.

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