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Advances in Nano Research
  Volume 4, Number 1, March 2016 , pages 031-44
DOI: https://doi.org/10.12989/anr.2016.4.1.031
 


Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory
Kaddour Rakrak, Mohamed Zidour, Houari Heireche, Abdelmoumen Anis Bousahla and Awda Chemi

 
Abstract
    This article is concerned with the free vibration problem for chiral double-walled carbon nanotube (DWCNTs) modelled using the non-local elasticity theory and Euler Bernoulli beam model. According to the governing equations of non-local Euler Bernoulli beam theory and the boundary conditions, the analytical solution is derived and two branches of transverse wave propagating are obtained. The numerical results obtained provide better representations of the vibration behaviour of double-walled carbon nanotube, where the aspect ratio of the (DWCNTs), the vibrational mode number, the small-scale coefficient and chirality of double-walled carbon nanotube on the frequency ratio (xN) of the (DWCNTs) are significant. In this work, the numerical results obtained can be used to predict and prevent the phenomenon of resonance for the forced vibration analyses of double -walled carbon nanotubes.
 
Key Words
    free vibration; double-walled carbon nanotube; frequency ratio; chirality; non-local
 
Address
Kaddour Rakrak: Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algerie; Département de Physique, Faculté des Sciences, Université Hassiba benbouali, Chlef, Algerie
Mohamed Zidour: Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbés, BP 89 Cité Ben M\'hidi, 22000 Sidi Bel Abbés, Algerie; Université Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algerie
Houari Heireche, Abdelmoumen Anis Bousahla and Awda Chemi: Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algerie
 

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