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.

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.

scholarly journals Nonlocal Euler-Bernoulli Beam Theories with Material Nonlinearity and their Application to Single-Walled Carbon Nanotubes

2021 ◽  
Author(s):  
kun huang ◽  
Benning Qu ◽  
Wei Xu ◽  
Ji Yao
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Scale Effect ◽  
Single Walled Carbon Nanotubes ◽  
Material Nonlinearity ◽  
Small Scale ◽  
Softening Effect ◽  
Single Walled Carbon ◽  
Small Scale Effect ◽  
Walled Carbon Nanotubes

Abstract The small-scale effect and the material nonlinearity significantly impact the mechanical properties of nanobeams. However, the combined effects of two factors have not attracted the attention of researchers. In the present paper, under the displacement’s Euler-Bernoulli assumption, we proposed two new nonlocal models to describe the mechanical properties of slender nanobeams for two centroid locus conditions: the locus extensibility and the locus inextensibility. Two new theories consider both the material nonlinearity and the small-scale effect induced by the non-local effect. The new models are used to analyze the static bending and the forced vibration for single-walled carbon nanotubes (SWCNTs). The results indicate that the stiffness’ softening effect induced by the material nonlinearity has more prominent impact than the nonlocal effect on SWCNT’s mechanical properties. Therefore, neglecting the material nonlinearity may cause qualitative mistakes.

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