scholarly journals Finite element formulation for the free vibration analysis of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory

2013 ◽  
Vol 7 (1) ◽  
pp. 6 ◽  
Author(s):  
Milad Hemmatnezhad ◽  
Reza Ansari
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Element Formulation ◽  
Nonlocal Timoshenko Beam Theory ◽  
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.

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