Wave propagation in double-walled carbon nanotubes on a novel analytically 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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Buckling and postbuckling of single-walled carbon nanotubes based on a nonlocal Timoshenko beam model

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik ◽

10.1002/zamm.201300017 ◽

2014 ◽

Vol 95 (9) ◽

pp. 939-951 ◽

Cited By ~ 14

Author(s):

R. Ansari ◽

M. Faghih Shojaei ◽

V. Mohammadi ◽

R. Gholami ◽

H. Rouhi

Keyword(s):

Carbon Nanotubes ◽

Timoshenko Beam ◽

Single Walled Carbon Nanotubes ◽

Beam Model ◽

Timoshenko Beam Model ◽

Single Walled Carbon ◽

Walled Carbon Nanotubes

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Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes

Journal of Sound and Vibration ◽

10.1016/j.jsv.2006.01.005 ◽

2006 ◽

Vol 294 (4-5) ◽

pp. 1060-1072 ◽

Cited By ~ 179

Author(s):

C.M. Wang ◽

V.B.C. Tan ◽

Y.Y. Zhang

Keyword(s):

Carbon Nanotubes ◽

Timoshenko Beam ◽

Vibration Analysis ◽

Beam Model ◽

Timoshenko Beam Model ◽

Multi Walled Carbon Nanotubes ◽

Walled Carbon Nanotubes

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Effects of Axial Load on Wave Propagation in Double-Walled Carbon Nanotubes Used as a Flexible Tip in AFM

Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2005-84549 ◽

2005 ◽

Author(s):

H. Dalir ◽

J. Akbari ◽

T. Hatsuzawa ◽

A. Farshidianfar

Keyword(s):

Wave Propagation ◽

Axial Load ◽

Wave Speed ◽

Critical Frequency ◽

Beam Model ◽

Timoshenko Beam Model ◽

Euler Beam ◽

Wave Speeds ◽

Double Walled Carbon Nanotubes ◽

Walled Carbon Nanotubes

This paper is concerned with the effect of axial load, shear deformation and rotary inertia on wave propagation in double-walled carbon nanotubes (DWCNTs) within terahertz range. Our analysis is based on Timoshenko-beam model and Euler-beam model. The present models predict some terahertz critical frequencies at which the number of wave speeds changes. In these models the amounts of wave speed is unique only when the frequency is below the lowest critical frequency. When the frequency is equal to the lowest critical frequency, there can be one or two (for CNTs of smaller radii) wave speeds. Furthermore, when the frequency is higher than the lowest critical frequency, more than one wave speed exists and waves of given frequency could propagate at various speeds. It can be seen that rotary inertia and shear deformation have a significant effect on both the wave speeds and the critical frequencies. Hence, terahertz wave propagation in CNTs should be better modeled by Timoshenko-beam model, instead of Euler-beam model.

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