Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal Timoshenko beam model

In this paper, the influence of van der Waals force on the wave propagation in viscoelastic double-walled carbon nanotubes (DWCNTs) is investigated. The governing equations of wave motion are derived based on the nonlocal strain gradient theory and double-walled Timoshenko beam model. The effects of viscosity, van der Waals force, as well as size effects on the wave propagation in DWCNTs are clarified. The results show that effects of van der Waals force on waves in inner and outer layers of DWCNTs are different. Flexural wave (FW) in outer layer and shear wave (SW) in inner layer are sensitive to van der Waals force, and display new phenomena. This new finding may provide some useful guidance in the acoustic design of nanostructures with DWCNTs as basic elements.

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

Proceedings of the Institution of Mechanical Engineers Part N Journal of Nanomaterials Nanoengineering and Nanosystems ◽

10.1177/2397791420931701 ◽

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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Influence of Thermal and Magnetic Field on Vibration of Double Walled Carbon Nanotubes Using Nonlocal Timoshenko Beam Theory

Procedia Materials Science ◽

10.1016/j.mspro.2015.06.047 ◽

2015 ◽

Vol 10 ◽

pp. 243-253 ◽

Cited By ~ 8

Author(s):

P. Ponnusamy ◽

A. Amuthalakshmi

Keyword(s):

Magnetic Field ◽

Carbon Nanotubes ◽

Timoshenko Beam ◽

Beam Theory ◽

Timoshenko Beam Theory ◽

Nonlocal Timoshenko Beam Theory ◽

Double Walled Carbon Nanotubes ◽

Walled Carbon Nanotubes

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Variational Principles for Vibrating Carbon Nanotubes Conveying Fluid, Based on the Nonlocal Beam Model

East Asian Journal on Applied Mathematics ◽

10.4208/eajam.130814.250515a ◽

2015 ◽

Vol 5 (3) ◽

pp. 209-221 ◽

Cited By ~ 3

Author(s):

Sarp Adali

Keyword(s):

Carbon Nanotubes ◽

Variational Principles ◽

Linear Time ◽

Scale Effects ◽

Time Dependent ◽

Small Scale ◽

Beam Model ◽

Geometric Boundary ◽

Double Walled Carbon Nanotubes ◽

Walled Carbon Nanotubes

AbstractVariational principles are derived in order to facilitate the investigation of the vibrations and stability of single and double-walled carbon nanotubes conveying a fluid, from a linear time-dependent partial differential equation governing their displacements. The nonlocal elastic theory of Euler-Bernoulli beams takes small-scale effects into account. Hamilton’s principle is obtained for double-walled nano-tubes conveying a fluid. The natural and geometric boundary conditions identified are seen to be coupled and time-dependent due to nonlocal effects.

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