Buckling Analysis of Multi-Walled Carbon Nanotubes with Consideration of Small Scale Effects

2011 ◽  
Vol 8 (11) ◽  
pp. 2214-2219 ◽  
Author(s):  
A. Tourki Samaei ◽  
M. M. Mirsayar
Keyword(s):  
Carbon Nanotubes ◽  
Scale Effects ◽  
Buckling Analysis ◽  
Small Scale ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Thermal Buckling of Multi-Walled Carbon Nanotubes by Nonlocal Elasticity

2006 ◽  
Vol 74 (3) ◽  
pp. 399-405 ◽  
Author(s):  
Renfu Li ◽  
George A. Kardomateas
Keyword(s):  
Carbon Nanotubes ◽  
Thermal Loading ◽  
Scale Effects ◽  
Elastic Shell ◽  
Thermal Buckling ◽  
Small Scale ◽  
Internal Length ◽  
Internal Characteristic ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

The small internal length scales of nanomaterials/nano-devices may call the direct application of classical continuum models into question. In this research, a nonlocal elastic shell model, which takes the small scale effects into account, is developed to study the thermal buckling behavior of multi-walled carbon nanotubes. The multi-walled carbon nanotubes are considered as concentric thin shells coupled with the van der Waals forces between adjacent nanotubes. Closed form solutions are formulated for two types of thermal buckling of a double-walled carbon nanotube: Radial thermal buckling (as in a shell under external pressure) and axial thermal buckling. The effects of small scale effects are demonstrated, and a significant influence of internal characteristic parameters such as the length of the C‐C bond has been found on the thermal buckling critical temperature. The study interestingly shows that the axial buckling is not likely to happen, while the “radial” buckling may often take place when the carbon nano-tubes are subjected to thermal loading. Furthermore, a convenient method to determine the material constant, “e0” and the internal characteristic parameter, “a,” is suggested.

Variational Principles for Vibrating Carbon Nanotubes Conveying Fluid, Based on the Nonlocal Beam Model

2015 ◽  
Vol 5 (3) ◽  
pp. 209-221 ◽  
Author(s):  
Sarp Adali
Keyword(s):  
Carbon Nanotubes ◽  
Variational Principles ◽  
Linear Time ◽  
Scale Effects ◽  
Time Dependent ◽  
Small Scale ◽  
Beam Model ◽  
Geometric Boundary ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

AbstractVariational principles are derived in order to facilitate the investigation of the vibrations and stability of single and double-walled carbon nanotubes conveying a fluid, from a linear time-dependent partial differential equation governing their displacements. The nonlocal elastic theory of Euler-Bernoulli beams takes small-scale effects into account. Hamilton’s principle is obtained for double-walled nano-tubes conveying a fluid. The natural and geometric boundary conditions identified are seen to be coupled and time-dependent due to nonlocal effects.

Analytical Treatment of the Free Vibration of Single-Walled Carbon Nanotubes Based on the Nonlocal Flugge Shell Theory

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
R. Ansari ◽  
H. Rouhi
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Scale Effects ◽  
Elastic Shell ◽  
Nonlocal Parameter ◽  
Single Walled Carbon Nanotubes ◽  
Small Scale ◽  
Resonant Frequencies ◽  
Single Walled Carbon ◽  
Walled Carbon Nanotubes

In the current work, the vibration characteristics of single-walled carbon nanotubes (SWCNTs) under different boundary conditions are investigated. A nonlocal elastic shell model is utilized, which accounts for the small scale effects and encompasses its classical continuum counterpart as a particular case. The variational form of the Flugge type equations is constructed to which the analytical Rayleigh–Ritz method is applied. Comprehensive results are attained for the resonant frequencies of vibrating SWCNTs. The significance of the small size effects on the resonant frequencies of SWCNTs is shown to be dependent on the geometric parameters of nanotubes. The effectiveness of the present analytical solution is assessed by the molecular dynamics simulations as a benchmark of good accuracy. It is found that, in contrast to the chirality, the boundary conditions have a significant effect on the appropriate values of nonlocal parameter.

Dynamics Instability Analysis of Multi-Walled Carbon Nanotubes Conveying Fluid

2013 ◽  
Vol 682 ◽  
pp. 153-160 ◽  
Author(s):  
A. Azrar ◽  
L. Azrar ◽  
A.A. Aljinadi ◽  
M. Hamadiche
Keyword(s):  
Carbon Nanotubes ◽  
Dynamic Instability ◽  
Fluid Velocity ◽  
Nonlocal Elasticity Theory ◽  
Model Potential ◽  
Small Scale ◽  
Instability Analysis ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
Conveying Fluid

The dynamic instability analysis of conveying fluid multi-walled carbon nanotubes (MWCNT) is analyzed. Based on the nonlocal elasticity theory, Donnells shell model, potential flow theory and the van der Waal interaction between walls, the governing equations are formulated. The small scale parameter and the internal fluid interaction effects on the dynamic behaviors of the MWCNT-fluid system as well as the instabilities induced by the fluid velocity are investigated. The critical velocity and the frequency-amplitude relationships are obtained with respect to physical and material parameters.

scholarly journals Detection of Multi-walled Carbon Nanotubes and Carbon Nanodiscs on Workplace Surfaces at a Small-Scale Producer

2015 ◽  
Vol 59 (7) ◽  
pp. 836-852 ◽  
Author(s):  
Maria Hedmer ◽  
Linus Ludvigsson ◽  
Christina Isaxon ◽  
Patrik T. Nilsson ◽  
Vidar Skaug ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Small Scale ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

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.

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