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Dynamic instability of vibrating carbon nanotubes near small layers of graphite sheets based on nonlocal continuum elasticity

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Abstract

This article presents a new asymptotic method to predict dynamic pull-in instability of nonlocal clamped–clamped carbon nanotubes (CNTs) near graphite sheets. Nonlinear governing equations of carbon nanotubes actuated by an electric field are derived. With due allowance for the van der Waals effects, the pull-in instability and the natural frequency–amplitude relationship are investigated by a powerful analytical method, namely, the parameter expansion method. It is demonstrated that retaining two terms in series expansions is sufficient to produce an acceptable solution. The obtained results from numerical methods verify the strength of the analytical procedure. The qualitative analysis of system dynamics shows that the equilibrium points of the autonomous system include center points and unstable saddle points. The phase portraits of the carbon nanotube actuator exhibit periodic and homoclinic orbits.

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Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    H. M. Sedighi & A. Yaghootian

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  1. H. M. Sedighi
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  2. A. Yaghootian
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Correspondence to H. M. Sedighi.

Additional information

Original Russian Text © Hamid M. Sedighi, Amin Yaghootian.

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 57, No. 1, pp. 105–117, January–February, 2016. Original article submitted July 16, 2013; revision submitted November 20, 2013.

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Sedighi, H.M., Yaghootian, A. Dynamic instability of vibrating carbon nanotubes near small layers of graphite sheets based on nonlocal continuum elasticity. J Appl Mech Tech Phy 57, 90–100 (2016). https://doi.org/10.1134/S0021894416010107

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  • DOI: https://doi.org/10.1134/S0021894416010107

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