Nonlocal Timoshenko beam model for the large-amplitude vibrations of embedded multiwalled carbon nanotubes including thermal effects

2011 ◽  
Vol 43 (6) ◽  
pp. 1171-1178 ◽  
Author(s):  
R. Ansari ◽  
H. Ramezannezhad
Keyword(s):  
Carbon Nanotubes ◽  
Multiwalled Carbon Nanotubes ◽  
Timoshenko Beam ◽  
Thermal Effects ◽  
Large Amplitude ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Multiwalled Carbon ◽  
Large Amplitude Vibrations

Investigating vibrations of viscoelastic fluid-conveying carbon nanotubes resting on viscoelastic foundation using a nonlocal fractional Timoshenko beam model

2020 ◽  
pp. 239779142093170
Author(s):  
M Faraji Oskouie ◽  
R Ansari ◽  
H Rouhi
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Time Domain ◽  
Beam Model ◽  
Viscoelastic Foundation ◽  
Timoshenko Beam Model ◽  
Governing Equations ◽  
The Time Domain

On the basis of fractional viscoelasticity, the size-dependent free-vibration response of viscoelastic carbon nanotubes conveying fluid and resting on viscoelastic foundation is studied in this article. To this end, a nonlocal Timoshenko beam model is developed in the context of fractional calculus. Hamilton’s principle is applied in order to obtain the fractional governing equations including nanoscale effects. The Kelvin–Voigt viscoelastic model is also used for the constitutive equations. The free-vibration problem is solved using two methods. In the first method, which is limited to the simply supported boundary conditions, the Galerkin technique is employed for discretizing the spatial variables and reducing the governing equations to a set of ordinary differential equations on the time domain. Then, the Duffing-type time-dependent equations including fractional derivatives are solved via fractional integrator transfer functions. In the second method, which can be utilized for carbon nanotubes with different types of boundary conditions, the generalized differential quadrature technique is used for discretizing the governing equations on spatial grids, whereas the finite difference technique is used on the time domain. In the results, the influences of nonlocality, geometrical parameters, fractional derivative orders, viscoelastic foundation, and fluid flow velocity on the time responses of carbon nanotubes are analyzed.

scholarly journals Variational Principles for Multiwalled Carbon Nanotubes Undergoing Vibrations Based on Nonlocal Timoshenko Beam Theory

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Ismail Kucuk ◽  
Ibrahim S. Sadek ◽  
Sarp Adali
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Multiwalled Carbon Nanotubes ◽  
Timoshenko Beam ◽  
Variational Principles ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Small Scale ◽  
Multiwalled Carbon ◽  
Nonlocal Timoshenko Beam Theory

Variational principles are derived for multiwalled carbon nanotubes undergoing linear vibrations using the semi-inverse method with the governing equations based on nonlocal Timoshenko beam theory which takes small scale effects and shear deformation into account. Physical models based on the nonlocal theory approximate the nanoscale phenomenon more accurately than the local theories by taking small scale phenomenon into account. Variational formulation is used to derive the natural and geometric boundary conditions which give a set of coupled boundary conditions in the case of free boundaries which become uncoupled in the case of the local theory. Hamilton's principle applicable to this case is also given.

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.

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