• Advances in nano research
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• v.4 no.1
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• pp.31-44
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• 2016

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 (${\chi}^N$) 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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.1
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• pp.169-174
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• 2011

For a double-walled carbon nanotube resonator with a short outer nanotube, the free edge of the short outer wall plays an important role in the vibration of the long inner nanotube. For a double-walled carbon nanotube resonator with a short inner nanotube, the short inner nanotube can be considered as a flexible core, thus, the fundamental frequency is influenced by its length. In this paper, we analysis frequency variation in ultrahigh frequency nanomechanical resonators based on double-walled carbon nanotubes with different wall length. This results will widely apply to the realization of frequency devices controlling the length of the inner or outer nanotube.

• Structural Engineering and Mechanics
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• v.65 no.3
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• pp.335-342
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• 2018

The transverse free vibration of chiral double-walled carbon nanotube (DWCNTs) embedded in elastic medium is modeled by the non-local elasticity theory and Euler Bernoulli beam model. The governing equations are derived and the solutions of frequency are obtained. According to this study, the vibrational mode number, the small-scale coefficient, the Winkler parameter and chirality of double-walled carbon nanotube on the frequency ratio (xN) of the (DWCNTs) are studied and discussed. The new features of the vibration behavior of (DWCNTs) embedded in an elastic medium and the present solutions can be used for the static and dynamic analyses of double-walled carbon nanotubes.

• Structural Engineering and Mechanics
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• v.54 no.5
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• pp.987-998
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• 2015

In this paper, free vibrations of a clamped-clamped double-walled carbon nanotube (DWNT) under axial force is studied. By utilizing Euler-Bernoulli beam theory, each layer of DWNT is modeled as a beam. In this analysis, nonlinear form of interlayer van der Waals (vdW) forces and nonlinearities aroused from mid-plane stretching are also considered in the equations of motion. Further, direct application of multiple scales perturbation method is utilized to solve the obtained equations and to analyze free vibrations of the DWNT. Therefore, analytical expressions are found for vibrations of each layer. Linear and nonlinear natural frequencies of the system and vibration amplitude ratios of inner to outer layers are also obtained. Finally, the results are compared with the results obtained by Galerkin method.

• Advances in nano research
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• v.3 no.4
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• pp.193-206
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• 2015

The present paper investigate the elastic buckling of chiral double-walled carbon nanotubes (DWCNTs) under axial compression. Using the non-local elasticity theory, Timoshenko beam model has been implemented. According to the governing equations of non-local theory, the analytical solution is derived and the solution for non-local critical buckling loads is obtained. The numerical results show the influence of non-local small-scale coefficient, the vibrational mode number, the chirality of carbon nanotube and aspect ratio of the (DWCNTs) on non-local critical buckling loads of the (DWCNTs). The results indicate the dependence of non-local critical buckling loads on the chirality of single-walled carbon nanotube with increase the non-local small-scale coefficient, the vibrational mode number and aspect ratio of length to diameter.

• Advances in nano research
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• v.5 no.2
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• pp.179-192
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• 2017

The transverse vibration of double walled carbon nanotube (DWCNT) embedded in elastic medium with an initial imperfection is considered. In this paper, Timoshenko beam theory is employed. However the nonlocal theory is used for modeling the nano scale of nanotube. In addition, the governing Equations of motion are obtained utilizing the Hamilton's principle and simply-simply boundary conditions are assumed. Furthermore, the Navier method is used for determining the natural frequencies of DWCNT. Hence, some parameters such as nonlocality, curvature amplitude, Winkler and Pasternak elastic foundations and length of the curved DWCNT are analyzed and discussed. The results show that, the curvature amplitude causes to increase natural frequency. However, nonlocal coefficient and elastic foundations have important role in vibration behavior of DWCNT with imperfection.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.9 no.5
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• pp.1150-1153
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• 2008

The coupled oscillation of multi-walled carbon-nanotube (MWCNT) oscillators consisting of (5n, 5n) CNTs was investigated by molecular dynamics simulations. The results show that the inter-wall coupling leads to frequency splits. And there are consistently three primary frequency peaks for the quadric-walled, penta-walled and hexa-walled CNT oscillators. It is independent of the wall parameters, suggesting applications as triple-frequency generators. Furthermore, at least one of the primary frequencies of a MWCNT oscillator is lower than that of its double-walled counterpart.

• Journal of the Korean Vacuum Society
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• v.17 no.6
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• pp.566-575
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• 2008

We investigated the field emission characteristics from the planar field emitters made of double-walled carbon nanotubes (DWCNTs) synthesized by a catalytic chemical vapor deposition (CCVD) method. Transmission electron microscopy, Thermogravimetric and Raman analysis showed that the carbon materials have a low defect level in their atomic carbon structure, pointing to the synthesis of high-purity DWCNTs. For field emission properties of DWCNTs, the turn-on field of DWCNTs was $1.9\;V/{\mu}m$ and the current density was about $74\;mA/cm^2$ at $8.1\;V/{\mu}m$, which is sufficient for the applications of field emission displays and vacuum microelectronic devices. The DWCNT field emitters also exhibited a uniform field emission pattern and good field emission stability in a diode configuration.

• Carbon letters
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• v.14 no.3
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• pp.131-144
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• 2013

The carbon nanotube (CNT) represents one of the most unique inventions in the field of nanotechnology. CNTs have been studied closely over the last two decades by many researchers around the world due to their great potential in different fields. CNTs are rolled graphene with $SP^2$ hybridization. The important aspects of CNTs are their light weight, small size with a high aspect ratio, good tensile strength, and good conducting characteristics, which make them useful as fillers in different materials such as polymers, metallic surfaces and ceramics. CNTs also have potential applications in the field of nanotechnology, nanomedicine, transistors, actuators, sensors, membranes, and capacitors. There are various techniques which can be used for the synthesis of CNTs. These include the arc-discharge method, chemical vaporize deposition (CVD), the laser ablation method, and the sol gel method. CNTs can be single-walled, double-walled and multi-walled. CNTs have unique mechanical, electrical and optical properties, all of which have been extensively studied. The present review is focused on the synthesis, functionalization, properties and applications of CNTs. The toxic effect of CNTs is also presented in a summarized form.

• Steel and Composite Structures
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• v.43 no.6
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• pp.797-808
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• 2022

This paper presents an investigation on the free vibration characteristics of functionally graded nanocomposite double-beams reinforced by single-walled carbon nanotubes (SWCNTs). The double-beams coupled by an interlayer spring, resting on the elastic foundation with a linear layer and shear layer, and is simply supported in thermal environments. The SWCNTs gradient distributed in the thickness direction of the beam forms different reinforcement patterns. The materials properties of the functionally graded carbon nanotube-reinforced composites (FG-CNTRC) are estimated by rule of mixture. The first order shear deformation theory and Euler-Lagrange variational principle are employed to derive the motion equations incorporating the thermal effects. The vibration characteristics under several patterns of reinforcement are presented and discussed. We conducted a series of studies aimed at revealing the effects of the spring stiffness, environment temperature, thickness ratios and carbon nanotube volume fraction on the nature frequency.