scholarly journals The Study of Modified van der Waals Interactions on Free Vibration of Multi-walled Carbon Nanotubes Using Multi-elastic Beam Model

2010 ◽  
Vol 20 (4) ◽  
pp. 390-396
Author(s):  
Ju-Il Yoon ◽  
S.W. Kang
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Van Der Waals ◽  
Elastic Beam ◽  
Van Der Waals Interactions ◽  
Beam Model ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

EFFECT OF THE VAN DER WAALS INTERACTION ON ANALYSIS OF DOUBLE-WALLED CARBON NANOTUBES

2005 ◽  
Vol 05 (03) ◽  
pp. 457-474 ◽  
Author(s):  
Q. WANG
Keyword(s):  
Carbon Nanotubes ◽  
Van Der Waals ◽  
Elastic Beam ◽  
Beam Model ◽  
Mechanical Models ◽  
Parametric Studies ◽  
Kink Instability ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
Vdw Interaction

This paper presents the research on the analysis of the van der Waals (vdW) interaction on double-walled carbon nanotubes (DWNTs) via an elastic beam model. The parametric studies on the size of DWNTs are conducted to show the effect of vdW interaction on the analysis of both a cantilever DWNT subjected to force at the free tip and a DWNT subjected to pure bending. In addition, the kink instability for the cantilever DWNT is analyzed based on the proposed beam model. It is hoped that the research will provide mechanical models for the analysis of both single-walled nanotubes (SWNTs) and multi-walled nanotubes (MWNTs), as well as for kink instability analysis of carbon nanotubes (CNTs).

SMALL SCALE EFFECT ON THE FREE VIBRATION OF MULTI-WALLED CARBON NANOTUBES

2008 ◽  
Vol 22 (28) ◽  
pp. 2769-2777 ◽  
Author(s):  
Y. YAN ◽  
W. Q. WANG ◽  
L. X. ZHANG
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Scale Effect ◽  
Large Scale ◽  
Small Scale ◽  
Beam Model ◽  
Aspect Ratios ◽  
Small Scale Effect ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

This paper is concerned with the free vibration of multi-walled carbon nanotubes (MWCNTs) with simply supported ends. Based on the non-local elasticity theory, Timoshenko beam model with the small scale effect and the van der Waals (vdW) interaction is derived and then solved analytically. The results reveal that the small scale effect is quite significant for small aspect ratios, large scale parameters and high radial vibration modes, whereas it is insensitive to the number of layers of MWCNTs and is weakly-dependent on the wall thickness of MWCNTs.

Effect of van der Waals force on wave propagation in viscoelastic double-walled carbon nanotubes

2018 ◽  
Vol 32 (24) ◽  
pp. 1850291
Author(s):  
Yugang Tang ◽  
Ying Liu
Keyword(s):  
Carbon Nanotubes ◽  
Wave Propagation ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Strain Gradient Theory ◽  
Flexural Wave ◽  
Gradient Theory ◽  
Beam Model ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this paper, the influence of van der Waals force on the wave propagation in viscoelastic double-walled carbon nanotubes (DWCNTs) is investigated. The governing equations of wave motion are derived based on the nonlocal strain gradient theory and double-walled Timoshenko beam model. The effects of viscosity, van der Waals force, as well as size effects on the wave propagation in DWCNTs are clarified. The results show that effects of van der Waals force on waves in inner and outer layers of DWCNTs are different. Flexural wave (FW) in outer layer and shear wave (SW) in inner layer are sensitive to van der Waals force, and display new phenomena. This new finding may provide some useful guidance in the acoustic design of nanostructures with DWCNTs as basic elements.

Finite Element Modeling of van der Waals Interaction for Elastic Stability of Multi-Walled Carbon Nanotubes

2008 ◽  
Vol 55-57 ◽  
pp. 525-528 ◽  
Author(s):  
Chawis Thongyothee ◽  
Somchai Chucheepsakul
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Van Der Waals ◽  
Compressive Force ◽  
Covalent Bond ◽  
Van Der Waals Force ◽  
Tube Length ◽  
Axial Compressive Force ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

The purpose of this study is to assess the effect of van der Waals interactions within multi-walled carbon nanotubes with the three dimensional finite element models. The elastic buckling behaviors of nanotubes are treated under axial compressive force acting on open both ends of nanotubes and considered with various boundary conditions. The analysis is based on the assumptions that the covalent bond of each wall is represented by an elastic beam element while the van der Waals force of adjacent walls are represented by a nonlinear truss element following the Lennard-Jones “6-12” theory. The models of double-walled carbon nanotubes are used to explain the characteristic of multi-walled carbon nanotubes and then results compared with the column theory. The results show that the critical load of nanotubes depends on atomic arrangement, tube length, and number of walls, while the van der Waals force has a small effect on the buckling load for multi-walled carbon nanotubes.

scholarly journals Free Vibration Analysis of DWCNTs Using CDM and Rayleigh-Schmidt Based on Nonlocal Euler-Bernoulli Beam Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Maria Anna De Rosa ◽  
Maria Lippiello
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Van Der Waals ◽  
Beam Theory ◽  
Van Der Waals Forces ◽  
Bernoulli Beam ◽  
Bernoulli Beam Theory ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
Euler Bernoulli Beam

The free vibration response of double-walled carbon nanotubes (DWCNTs) is investigated. The DWCNTs are modelled as two beams, interacting between them through the van der Waals forces, and the nonlocal Euler-Bernoulli beam theory is used. The governing equations of motion are derived using a variational approach and the free frequencies of vibrations are obtained employing two different approaches. In the first method, the two double-walled carbon nanotubes are discretized by means of the so-called “cell discretization method” (CDM) in which each nanotube is reduced to a set of rigid bars linked together by elastic cells. The resulting discrete system takes into account nonlocal effects, constraint elasticities, and the van der Waals forces. The second proposed approach, belonging to the semianalytical methods, is an optimized version of the classical Rayleigh quotient, as proposed originally by Schmidt. The resulting conditions are solved numerically. Numerical examples end the paper, in which the two approaches give lower-upper bounds to the true values, and some comparisons with existing results are offered. Comparisons of the present numerical results with those from the open literature show an excellent agreement.

Effect of van der Waals Interactions on the Raman Modes in Single Walled Carbon Nanotubes

2001 ◽  
Vol 86 (17) ◽  
pp. 3895-3898 ◽  
Author(s):  
A. M. Rao ◽  
J. Chen ◽  
E. Richter ◽  
U. Schlecht ◽  
P. C. Eklund ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Van Der Waals ◽  
Single Walled Carbon Nanotubes ◽  
Van Der Waals Interactions ◽  
Single Walled Carbon ◽  
Raman Modes ◽  
Walled Carbon Nanotubes
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