Nonlocal Timoshenko beam model for considering shear effect of van der Waals interactions on free vibration of multilayer graphene nanoribbons

2015 ◽  
Vol 133 ◽  
pp. 522-528 ◽  
Author(s):  
Reza Nazemnezhad
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Graphene Nanoribbons ◽  
Van Der Waals ◽  
Van Der Waals Interactions ◽  
Multilayer Graphene ◽  
Beam Model ◽  
Shear Effect ◽  
Timoshenko Beam Model

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.

Free Vibration Analysis of Carbon Nanotubes by Timoshenko Beam Model and Thin-Plate Spline Radial Basis Function

2013 ◽  
Vol 365-366 ◽  
pp. 1207-1210
Author(s):  
Feng Wang ◽  
Li Na Xu ◽  
Shu Bo Sui
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Radial Basis Function ◽  
Thin Plate ◽  
Timoshenko Beam ◽  
Basis Function ◽  
Thin Plate Spline ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Radial Basis

Timoshenko beam model and the meshless method based on thin-plate spline radial basis function are used to analyze the free vibration of carbon nanotubes. The natural frequencies of the carbon nanotubes with different length-to-diameter ratios and boudary conditions are compared with the results of published literatures which demonstrate the high accuracy of present method.

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.

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