Methods to model and simulate super carbon nanotubes of higher order

2016 ◽  
Vol 29 (7) ◽  
pp. e3872 ◽  
Author(s):  
Michael Burger ◽  
Christian Bischof ◽  
Christian Schröppel ◽  
Jens Wackerfuß
Keyword(s):  
Carbon Nanotubes ◽  
Higher Order

Higher-Order Elasticity Constants of Carbon Nanotubes

2013 ◽  
Vol 815 ◽  
pp. 516-519
Author(s):  
Bin Gao ◽  
Yu Zhou Sun ◽  
Shen Li
Keyword(s):  
Carbon Nanotubes ◽  
Cylindrical Tube ◽  
Higher Order ◽  
Constitutive Relationship ◽  
Atomic Interaction ◽  
Thin Wall ◽  
Single Walled Carbon Nanotube ◽  
Theoretical Scheme ◽  
Representative Cell ◽  
Brenner Potential

In this paper, the higher-order elasticity constants are evaluated in the theoretical scheme of higher-order continuum. A single-walled carbon nanotube is treated as a higher-order continuum cylindrical tube with a thin wall, and the representative cell is chosen as a triangle unit that contains four carbon atoms. The Brenner potential is employed to describe the C-C atomic interaction, and the higher-order constitutive relationship is derived by virtue of the higher-order Cauchy-Born rule. The higher-order elasticity constants of carbon nanotubes are evaluated based on the derived higher-order constitutive model, which can provide a foundation for the further analysis of the mechanical properties of carbon nanotubes in the theoretical scheme of higher-order continuum.

Terahertz Vibration of Short Carbon Nanotubes Modeled as Timoshenko Beams

2005 ◽  
Vol 72 (1) ◽  
pp. 10-17 ◽  
Author(s):  
J. Yoon ◽  
C. Q. Ru ◽  
A. Mioduchowski
Keyword(s):  
Carbon Nanotubes ◽  
Aspect Ratio ◽  
Timoshenko Beam ◽  
Large Diameter ◽  
Higher Order ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Double Beam ◽  
Short Carbon ◽  
Double Wall

Short carbon nanotubes of smaller aspect ratio (say, between 10 and 50) are finding significant application in nanotechnology. This paper studies vibration of such short carbon nanotubes whose higher-order resonant frequencies fall within terahertz range. Because rotary inertia and shear deformation are significant for higher-order modes of shorter elastic beams, the carbon nanotubes studied here are modeled as Timoshenko beams instead of classical Euler beams. Detailed results are demonstrated for double-wall carbon nanotubes of aspect ratio 10, 20, or 50 based on the Timoshenko-beam model and the Euler-beam model, respectively. Comparisons between different single-beam or double-beam models indicate that rotary inertia and shear deformation, accounted for by the Timoshenko-beam model, have a substantial effect on higher-order resonant frequencies and modes of double-wall carbon nanotubes of small aspect ratio (between 10 and 20). In particular, Timoshenoko-beam effects are significant for both large-diameter and small-diameter double-wall carbon nanotubes, while double-beam effects characterized by noncoaxial deflections of the inner and outer tubes are more significant for small-diameter than large-diameter double-wall carbon nanotubes. This suggests that the Timoshenko-beam model, rather than the Euler-beam model, is relevant for terahertz vibration of short carbon nanotubes.

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