Thermal Buckling of Multi-Walled Carbon Nanotubes by Nonlocal Elasticity

2006 ◽  
Vol 74 (3) ◽  
pp. 399-405 ◽  
Author(s):  
Renfu Li ◽  
George A. Kardomateas

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.

Author(s):  
R. Ansari ◽  
H. Rouhi

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.


2013 ◽  
Vol 80 (2) ◽  
Author(s):  
R. Ansari ◽  
B. Arash

In this paper, the vibrational behavior of double-walled carbon nanotubes (DWCNTs) is studied by a nonlocal elastic shell model. The nonlocal continuum model accounting for the small scale effects encompasses its classical continuum counterpart as a particular case. Based upon the constitutive equations of nonlocal elasticity, the displacement field equations coupled by van der Waals forces are derived. The set of governing equations of motion are then numerically solved by a novel method emerged from incorporating the radial point interpolation approximation within the framework of the generalized differential quadrature method. The present analysis provides the possibility of considering different combinations of layerwise boundary conditions. The influences of small scale factor, layerwise boundary conditions and geometrical parameters on the mechanical behavior of DWCNTs are fully investigated. Explicit expressions for the nonlocal frequencies of DWCNTs with all edges simply supported are also analytically obtained by a nonlocal elastic beam model. Some new intertube resonant frequencies and the corresponding noncoaxial vibrational modes are identified due to incorporating circumferential modes into the shell model. A shift in noncoaxial mode numbers, not predictable by the beam model, is also observed when the radius of DWCNTs is varied. The results generated also provide valuable information concerning the applicability of the beam model and new noncoaxial modes affecting the physical properties of nested nanotubes.


Author(s):  
Mohsen Asghari ◽  
Jacob Rafati

The nonlocal continuum theories are capable to reflect the small length characteristic of nanostructures. In this work, variational principles are presented for the stability analysis of multi-walled carbon nanotubes under various mechanical loadings based on the nonlocal elastic Donnell’s shell by the semi-inverse method. In this manner, a set of proper essential and natural boundary conditions for each layer of the multi-walled nanotube is derived.


2015 ◽  
Vol 5 (3) ◽  
pp. 209-221 ◽  
Author(s):  
Sarp Adali

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.


2013 ◽  
Vol 682 ◽  
pp. 153-160 ◽  
Author(s):  
A. Azrar ◽  
L. Azrar ◽  
A.A. Aljinadi ◽  
M. Hamadiche

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.


2015 ◽  
Vol 59 (7) ◽  
pp. 836-852 ◽  
Author(s):  
Maria Hedmer ◽  
Linus Ludvigsson ◽  
Christina Isaxon ◽  
Patrik T. Nilsson ◽  
Vidar Skaug ◽  
...  

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