Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models

2006 ◽  
Vol 357 (2) ◽  
pp. 130-135 ◽  
Author(s):  
Q. Wang ◽  
V.K. Varadan ◽  
S.T. Quek
Keyword(s):  
Carbon Nanotubes ◽  
Scale Effect ◽  
Continuum Models ◽  
Small Scale ◽  
Elastic Buckling ◽  
Nonlocal Continuum ◽  
Small Scale Effect

Small Scale Effect on Boundary Conditions of Cantilever Single Carbon Nanotubes

2013 ◽  
Vol 275-277 ◽  
pp. 33-37
Author(s):  
Ming Li ◽  
Hui Ming Zheng ◽  
Luo Xia ◽  
Liu Yang
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Condition ◽  
Boundary Conditions ◽  
Scale Effect ◽  
Nonlocal Elasticity ◽  
Small Scale ◽  
Euler Beam ◽  
Local Boundary ◽  
Local Boundary Condition ◽  
Small Scale Effect

In this paper, the boundary condition on free vibration of cantilever single-walled carbon nanotubes (SWCNTs) with Winkler elastic medium is investigated. The Euler beam theory with nonlocal elasticity is modeled as SWCNT. The analytical solution is derived and the numerical results show that the additional boundary conditions from small scale do not change natural frequencies. The reason is that the additional work made by the moment and shear force at the free end from small scale effect cancel each other, the boundary conditions due to local elasticity and nonlocal elasticity are also equivalent. Thus for simplicity, one can apply the local boundary condition to replace the small scale boundary condition.

Energy meaning of small-scale effect on free vibration of carbon nanotubes

2014 ◽  
Vol 10 (5/6) ◽  
pp. 415
Author(s):  
Li Ming ◽  
Zheng Huiming ◽  
Luo Xia ◽  
Liu Yang
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Scale Effect ◽  
Small Scale ◽  
Small Scale Effect

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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