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Differential quadrature solutions for the nonconservative instability of a class of single-walled carbon nanotubes

Maria Anna De Rosa (School of Engineering, University of Basilicata, Potenza, Italy)
Maria Lippiello (Department of Structures for Engineering and Architecture, University of Naples “Federico II”, Naples, Italy)
Stefania Tomasiello (CORISA and Department of Information, Electrical Engineering and Applied Mathematics, University of Salerno, Fisciano, Italy)

Engineering Computations

ISSN: 0264-4401

Article publication date: 5 March 2018

94

Abstract

Purpose

The purpose of the present paper is to investigate the nonconservative instability of a single-walled carbon nanotube (SWCNT) with an added mass through nonlocal theories. The governing equations are discretized by means of the differential quadrature (DQ) rules, as introduced by Bellman and Casti. DQ rules have been largely used in engineering and applied sciences. Recently, they were applied to enhance some numerical schemes, such as step-by-step integration schemes and Picard-like numerical schemes.

Design/methodology/approach

In the present paper, the DQ rules are used to investigate the nonconservative instability of a SWCNT through nonlocal theories.

Findings

To show the sensitivity of the SWCNT to the values of added mass and the influence of nonlocal parameter on the fundamental frequencies values, some numerical examples have been performed and discussed. Yet, the effect of the different boundary conditions on the instability behaviour has been investigated. The validity of the present model has been confirmed by comparing some results against the ones available in literature.

Originality/value

Applying the nonlocal elasticity theory, this paper presents a re-formulation of Hamilton’s principle for the free vibration analysis of a uniform Euler–Bernoulli nanobeam. The main purpose of this paper is to investigate the free vibration response of an SWCNT with attached mass and for various values of small scale effects.

Keywords

Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive comments and precious suggestions on the original version of the paper.

Citation

De Rosa, M.A., Lippiello, M. and Tomasiello, S. (2018), "Differential quadrature solutions for the nonconservative instability of a class of single-walled carbon nanotubes", Engineering Computations, Vol. 35 No. 1, pp. 251-267. https://doi.org/10.1108/EC-12-2016-0427

Publisher

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Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited

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