Transverse waves propagating in carbon nanotubes via a higher-order nonlocal beam model

2013 ◽  
Vol 95 ◽  
pp. 328-336 ◽  
Author(s):  
Y. Huang ◽  
Q.-Z. Luo ◽  
X.-F. Li
Keyword(s):  
Carbon Nanotubes ◽  
Higher Order ◽  
Beam Model ◽  
Transverse Waves ◽  
Nonlocal Beam

Scale Coefficient, Length, Mode and Radius Effect on Critical Axial Compressed Buckling Load of Carbon Nanotubes via Nonlocal Continuum Model

2012 ◽  
Vol 629 ◽  
pp. 296-301
Author(s):  
Hong Liang Tian
Keyword(s):  
Carbon Nanotubes ◽  
Continuum Model ◽  
Elastic Shell ◽  
Elastic Beam ◽  
Analytic Solutions ◽  
Buckling Load ◽  
Beam Model ◽  
Mechanical Behaviors ◽  
Nonlocal Beam ◽  
Scale Coefficient

Some exact concise analytic solutions of critical axial compressed buckling load for carbon nanotubes are derived via nonlocal beam. Scale coefficient, length, mode and radius effect on nonlocal critical axial compressed buckling load of CNTs is established and can be analyzed in terms of the general solutions. Radius effect on nonlocal critical axial compressed buckling load is only found through nonlocal elastic shell model but not derived via nonlocal elastic beam model. Numerical calculations of CNTs show that local critical axial compressed buckling load through local elastic theory is overestimated. Scale coefficient, length, mode and radius effect should be taken into account in predicting more accurate results for mechanical behaviors of CNTs via continuum model.

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.

Nonlocal beam model for axial buckling of carbon nanotubes with surface effect

2012 ◽  
Vol 99 (5) ◽  
pp. 56007 ◽  
Author(s):  
Yu-Gang Sun ◽  
Xiao-Hu Yao ◽  
Ying-Jing Liang ◽  
Qiang Han
Keyword(s):  
Carbon Nanotubes ◽  
Surface Effect ◽  
Beam Model ◽  
Axial Buckling ◽  
Nonlocal Beam

scholarly journals Beam Theory of Thermal–Electro-Mechanical Coupling for Single-Wall Carbon Nanotubes

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 923
Author(s):  
Kun Huang ◽  
Ji Yao
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Beam Theory ◽  
Bending Stiffness ◽  
Single Wall Carbon Nanotubes ◽  
Beam Model ◽  
Euler Beam ◽  
New Model ◽  
Mechanical Coupling ◽  
Electrostatic Fields

The potential application field of single-walled carbon nanotubes (SWCNTs) is immense, due to their remarkable mechanical and electrical properties. However, their mechanical properties under combined physical fields have not attracted researchers’ attention. For the first time, the present paper proposes beam theory to model SWCNTs’ mechanical properties under combined temperature and electrostatic fields. Unlike the classical Bernoulli–Euler beam model, this new model has independent extensional stiffness and bending stiffness. Static bending, buckling, and nonlinear vibrations are investigated through the classical beam model and the new model. The results show that the classical beam model significantly underestimates the influence of temperature and electrostatic fields on the mechanical properties of SWCNTs because the model overestimates the bending stiffness. The results also suggest that it may be necessary to re-examine the accuracy of the classical beam model of SWCNTs.

scholarly journals Torsional Characteristics of Carbon Nanotubes: Micropolar Elasticity Models and Molecular Dynamics Simulation

Nanomaterials ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 453
Author(s):  
Razie Izadi ◽  
Meral Tuna ◽  
Patrizia Trovalusci ◽  
Esmaeal Ghavanloo
Keyword(s):  
Carbon Nanotubes ◽  
Molecular Dynamics ◽  
Scale Effects ◽  
Couple Stress Theory ◽  
Dynamics Simulation ◽  
Local Theory ◽  
Beam Model ◽  
Specific Class ◽  
Micropolar Theory ◽  
Material Parameters

Efficient application of carbon nanotubes (CNTs) in nano-devices and nano-materials requires comprehensive understanding of their mechanical properties. As observations suggest size dependent behaviour, non-classical theories preserving the memory of body’s internal structure via additional material parameters offer great potential when a continuum modelling is to be preferred. In the present study, micropolar theory of elasticity is adopted due to its peculiar character allowing for incorporation of scale effects through additional kinematic descriptors and work-conjugated stress measures. An optimisation approach is presented to provide unified material parameters for two specific class of single-walled carbon nanotubes (e.g., armchair and zigzag) by minimizing the difference between the apparent shear modulus obtained from molecular dynamics (MD) simulation and micropolar beam model considering both solid and tubular cross-sections. The results clearly reveal that micropolar theory is more suitable compared to internally constraint couple stress theory, due to the essentiality of having skew-symmetric stress and strain measures, as well as to the classical local theory (Cauchy of Grade 1), which cannot accounts for scale effects. To the best of authors’ knowledge, this is the first time that unified material parameters of CNTs are derived through a combined MD-micropolar continuum theory.

scholarly journals Investigation of failure initiation in curved composite laminates using a higher-order beam model

2017 ◽  
Vol 168 ◽  
pp. 143-152 ◽  
Author(s):  
C. Thurnherr ◽  
R.M.J. Groh ◽  
P. Ermanni ◽  
P.M. Weaver
Keyword(s):  
Composite Laminates ◽  
Higher Order ◽  
Beam Model ◽  
Failure Initiation

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.

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
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