Buckling of a Clamped-Free Double-Walled Carbon Nanotube by the Bubnov-Galerkin Method

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
Isaac Elishakoff ◽  
Simon Bucas
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Galerkin Method ◽  
Compressive Load ◽  
Comparison Functions ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

This study deals with the Bubnov-Galerkin method applied to the buckling of clamped-free double-walled carbon nanotubes (DWCNTs) subjected to a concentrated compressive load at the free end. It was found that at least four comparison functions are needed in order to obtain accurate results.

Effective Approximations for Natural Frequencies of Double-Walled Carbon Nanotubes Based on Donnell Shell Theory

2011 ◽  
Vol 2 (2) ◽  
Author(s):  
Demetris Pentaras ◽  
Isaac Elishakoff
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Natural Frequency ◽  
Characteristic Equation ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Analytical Formulas ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
First Time

The vibration behavior of double-walled carbon nanotube (DWCNT) is investigated based on Donnell shell theory with van der Waals interaction taken into consideration. In addition, new results are obtained for the natural frequencies of a DWCNT based on a simplified version of Donnell shell theory by neglecting the tangential inertia terms. The resulting reduced characteristic equation for the natural frequency represents the radial mode of vibration. The factor of neglecting tangential inertia relative to the values of frequencies obtained by full Donnell shell theory is also obtained with attendant interesting results. Further possible simplifications of Donnell shell theory are introduced. For the first time in the literature, the effect of neglect of tangential inertia terms in DWCNTs is investigated. Accurate approximate analytical formulas are uncovered for the fundamental natural frequencies and compared with the exact values.

scholarly journals Nanomechanics of Nonideal Single- and Double-Walled Carbon Nanotubes

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
C. H. Wong ◽  
V. Vijayaraghavan
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Inner Core ◽  
Simulation Method ◽  
Dynamics Simulation ◽  
Tube Axis ◽  
Nonbonded Interactions ◽  
High Performing ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

The buckling characteristics of nonideal single- and double-walled carbon nanotubes were studied in this work via molecular dynamics simulation method. An imperfectly straight nonideal single-walled carbon nanotube (SWCNT) with a bent along the tube axis was used to form an array which is subjected to compression. The change in orientation of bends will result in a variation of nonbonded interactions in an SWCNT array system. We find that these variations in the nonbonded interactions strongly affect the buckling resistance of the SWCNT array. Similarly, a nonideal double-walled carbon nanotube (DWCNT) is constructed by varying the interlayer distance by introducing a center offset on the inner core SWCNT. The inclusion of offset along the tube axis in such nonideal DWCNT can enhance or deteriorate the mechanical qualities of the DWCNT under compression. Our numerical studies on nonideal CNT systems suggest a possibility of designing high-performing CNTs for applications involving fiber reinforcements.

scholarly journals Buckling of double-walled carbon nanotubes

2012 ◽  
Vol 34 (4) ◽  
pp. 217-224 ◽  
Author(s):  
Isaac Elishakoff ◽  
Kévin Dujat ◽  
Maurice Lemaire
Keyword(s):  
Carbon Nanotubes ◽  
Exact Solution ◽  
Approximate Solution ◽  
Carbon Nanotube ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Simply Supported ◽  
The Finite Difference Method ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this note we deal with the approximate solution of the buckling problem of a clamped-free double-walled carbon nanotube. First the finite difference method is utilized to solve this case. Then this approach is verified by solving the buckling problem of a double-walled carbon nanotube that is simply supported at both ends for which the exact solution is available.

scholarly journals Carbon nanotube ecotoxicity in amphibians: assessment of multiwalled carbon nanotubes and comparison with double-walled carbon nanotubes

Nanomedicine ◽  
2010 ◽  
Vol 5 (6) ◽  
pp. 963-974 ◽  
Author(s):  
Florence Mouchet ◽  
Perine Landois ◽  
Pascal Puech ◽  
Eric Pinelli ◽  
Emmanuel Flahaut ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Multiwalled Carbon Nanotubes ◽  
Multiwalled Carbon ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

FREE VIBRATION ANALYSIS OF DOUBLE-WALLED CARBON NANOTUBES USING THE SMOOTHED FINITE ELEMENT METHOD

2011 ◽  
Vol 08 (04) ◽  
pp. 879-890 ◽  
Author(s):  
LIFENG WANG ◽  
DONG HAN ◽  
G. R. LIU ◽  
XIANGYANG CUI
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Van Der Waals Interactions ◽  
Euler Beam ◽  
Resonant Frequencies ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

This paper studies the resonant frequencies and the associated vibration modes of an individual double-walled carbon nanotube, using gradient smoothing technique. The study uses a double-elastic beam based on the Euler beam theory with the consideration of the intertube van der Waals interactions. A gradient smoothed formulation is deployed to deal with the fourth-order differential equation of the Euler beam problems for dynamic analysis of the double-walled carbon nanotubes. In the double-thin beam problems, a set of linear shape functions are adopted to approximate the displacement field. Smoothing domains are then formed for computing the smoothed curvature and bending moment field. Compared with analysis results of multi-beam theory, numerical examples indicate that very accurate results could be yielded when a reasonable number of nodes were used. The results also showed that non-coaxial intertube resonance would be excited at the higher resonant frequencies of double-walled carbon nanotubes. In addition, free vibration of a double-walled carbon nanotube with inner wall simple supported and outer wall one end fixed and the other end free is studied.

Damping Characteristics of Commensurate Double-Walled Carbon Nanotube Oscillators

2007 ◽  
Vol 1057 ◽  
Author(s):  
Y. Ooi ◽  
K. Shintani
Keyword(s):  
Carbon Nanotubes ◽  
Molecular Dynamics ◽  
Carbon Nanotube ◽  
Energy Dissipation ◽  
Md Simulation ◽  
Tube Length ◽  
Damping Characteristics ◽  
Damped Oscillations ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

ABSTRACTThe intertube oscillations of double-walled carbon nanotubes (DWNTs) are investigated using molecular-dynamics (MD) simulation. The inner and outer tubes of model DWNTs have chiral indices of armchair type. The intertube oscillations are damped owing to energy dissipation. The logarithmic decrements and frequencies of the damped oscillations are calculated. The results show that the logarithmic decrement increases with increasing the tube diameter and decreases with increasing the tube length.

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