Free flexural vibration studies of double-walled carbon nanotubes with different boundary conditions and modeled as nonlocal Euler beams via the Galerkin method

2009 ◽  
Vol 106 (9) ◽  
pp. 094307 ◽  
Author(s):  
A. Shakouri ◽  
R. M. Lin ◽  
T. Y. Ng
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Galerkin Method ◽  
Flexural Vibration ◽  
Different Boundary Conditions ◽  
The Galerkin Method ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Vibrations of Double-Walled Carbon Nanotubes With Different Boundary Conditions Between Inner and Outer Tubes

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
Kai-Yu Xu ◽  
Elias C. Aifantis ◽  
Yong-Hua Yan
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Resonant Frequency ◽  
Free Vibrations ◽  
Original Method ◽  
Reduced Form ◽  
Vibrational Modes ◽  
Resonant Frequencies ◽  
Different Boundary Conditions ◽  
Double Walled Carbon Nanotubes

Free vibrations of a double-walled carbon nanotube (DWNT) are studied. The inner and outer carbon nanotubes are modeled as two individual elastic beams interacting each other by van der Waals forces. An original method is proposed to calculate the first seven order resonant frequencies and relative vibrational modes. Detailed results are demonstrated for DWNTs according to the different boundary conditions between inner and outer tubes, such as fixed-free, cantilever-free, fixed-simple and fixed-fixed (reduced form) supported ends. Our results indicate that there is a special invariable frequency for a DWNT that is not affected by different combinations of boundary conditions. All vibrational modes of the DWNT must be coaxial when the resonant frequency is smaller than this frequency. Some noncoaxial vibrations will occur when their resonant frequencies exceed the frequency. Especially, the first noncoaxial resonant frequency is still invariable for all different boundary conditions. A change of resonant frequency for various lengths of DWNTs is discussed in detail. In addition, our model predicts a new coaxial-noncoaxial vibrational mode in fixed-simple supports for inner and outer tubes of a DWNT.

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.

NONLOCAL ANALYTICAL FLUGGE SHELL MODEL FOR AXIAL BUCKLING OF DOUBLE-WALLED CARBON NANOTUBES WITH DIFFERENT END CONDITIONS

NANO ◽  
2012 ◽  
Vol 07 (03) ◽  
pp. 1250018 ◽  
Author(s):  
HESSAM ROUHI ◽  
REZA ANSARI
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Shell Model ◽  
Ritz Method ◽  
Nonlocal Parameter ◽  
Geometrical Parameters ◽  
Field Equations ◽  
Axial Buckling ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this paper, a nonlocal Flugge shell model is utilized to investigate the axial buckling behavior of double-walled carbon nanotubes (DWCNTs) under various boundary conditions. According to the nonlocal elasticity theory, the displacement field equations coupled by the van der Waals interaction are derived. The set of governing equations of motion is then solved by the Rayleigh–Ritz method. The present analysis can treat boundary conditions in a layer-wise manner. The effects of nonlocal parameter, layer-wise boundary conditions and geometrical parameters on the mechanical behavior of DWCNTs are examined. Furthermore, molecular dynamics simulations are performed to assess the validity of the results and also to predict the appropriate values of nonlocal parameter. It is found that the type of boundary conditions affects the proper value of nonlocal parameter.

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