scholarly journals Free vibration of a single-walled carbon nanotube based on the nonlocal Timoshenko beam model

2021 ◽  
Vol 37 ◽  
pp. 616-635
Author(s):  
Yu-Chi Su ◽  
Tse-Yu Cho
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Elastic Medium ◽  
Timoshenko Beam ◽  
Slenderness Ratio ◽  
Mode Shapes ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon

Abstract Free vibration of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium is studied on the basis of the nonlocal Timoshenko beam model. Influences of the slenderness ratios, the boundary conditions, the atomic structures and the stiffness of the embedded medium on the natural frequencies and mode shapes of SWCNT are examined. The nonlocal effect is significant for the higher modes of SWCNT with a small slenderness ratio embedded in a soft elastic medium, and it softens the SWCNT except for the fundamental frequency of the clamped–free SWCNT.

Chaotic vibrations of a harmonically excited carbon nanotube with consideration of thermomagnetic filed and surface effects

2019 ◽  
Vol 233 (10) ◽  
pp. 3649-3658 ◽  
Author(s):  
H Ramezannejad Azarboni ◽  
SA Edalatpanah
Keyword(s):  
Carbon Nanotube ◽  
Dynamic Response ◽  
Governing Equation ◽  
Surface Effect ◽  
Time History ◽  
Integration Scheme ◽  
Beam Model ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Chaotic Vibrations

In the studies of the dynamic response of carbon nanotubes, the stability, predictable, and unpredictable chaotic vibrations are fundamental characteristics. In this paper, we investigate the chaotic and periodic vibrations of a single-walled carbon nanotube resting on the viscoelastic foundation, based on the nonlocal Euler–Bernoulli beam model. It is assumed that the single-walled carbon nanotube is subjected to an external harmonic excitation. The axial thermomagnetic field and the surface effect on the governing equation of single-walled carbon nanotube are taken into account. We also solve the nonlinear governing equation by using the Galerkin decomposition method along with the fourth-order Rung–Kutta numerical integration scheme. Furthermore, we analyze the effects of amplitude and frequency of excitation on the formation of chaotic and periodic regions using bifurcation diagrams and largest Lyapunov exponents. Moreover, we present the phase portrait, Poincare maps, and time history to observe the periodic and chaotic responses of the system. The results show that the nonlinear dynamic response of single-walled carbon nanotube is much more sensitive to both amplitude and frequency of excitation.

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.

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