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Torsional vibration of single-walled carbon nanotubes using doublet mechanics

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Abstract

This paper investigates the torsional vibration of single-walled carbon nanotubes (SWCNTs) using a new approach based on doublet mechanics (DM) incorporating explicitly scale parameter and chiral effects. A fourth-order partial differential equation that governs the torsional vibration of nanotubes is derived. Using DM, an explicit equation for the natural frequency in terms of geometrical and mechanical property of CNTs is obtained for both the Zigzag and Armchair nanotube for the torsional vibration mode. It is shown that chiral effects along with the scale parameter play a significant role in the vibration behavior of SWCNTs in torsional vibration mode. Such effects decrease the natural frequency obtained by DM compared to the classical continuum mechanics and nonlocal theory predictions. However, with increase in the length and/or the radius of the tube, the effect of the chiral and scale parameter on the natural frequency decreases.

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Authors and Affiliations

  1. Department of Mechanical Engineering, College of Engineering, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran

    Alireza Fatahi-Vajari

  2. Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Ali Imam

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  1. Alireza Fatahi-Vajari
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  2. Ali Imam
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Correspondence to Ali Imam.

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Fatahi-Vajari, A., Imam, A. Torsional vibration of single-walled carbon nanotubes using doublet mechanics. Z. Angew. Math. Phys. 67, 81 (2016). https://doi.org/10.1007/s00033-016-0675-6

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