Research on the nonlinear vibration of carbon nanotube embedded in fractal medium

Fractals ◽  
2021 ◽  
Author(s):  
Kang-Jia Wang
Keyword(s):  
Carbon Nanotube ◽  
Nonlinear Vibration ◽  
Fractal Medium

scholarly journals Study on the nonlinear vibration of embedded carbon nanotube via the Hamiltonian-based method

2021 ◽  
pp. 146134842110327
Author(s):  
Kang-Jia Wang ◽  
Guo-Dong Wang
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Nonlinear Vibration ◽  
Elastic Medium ◽  
Numerical Results ◽  
Frequency Property ◽  
New Novel ◽  
Novel Method

This article mainly studies the vibration of the carbon nanotubes embedded in elastic medium. A new novel method called the Hamiltonian-based method is applied to determine the frequency property of the nonlinear vibration. Finally, the effectiveness and reliability of the proposed method is verified through the numerical results. The obtained results in this work are expected to be helpful for the study of the nonlinear vibration.

scholarly journals Nonlinear Vibration of a Pre-Stressed Water-Filled Single-Walled Carbon Nanotube Using Shell Model

Nanomaterials ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 974
Author(s):  
Mahmoud Mohamed Selim ◽  
Awad Musa
Keyword(s):  
Carbon Nanotube ◽  
Nonlinear Vibration ◽  
Shell Theory ◽  
Analytical Formula ◽  
Water System ◽  
Nonlinear Frequency ◽  
Nonlinear Parameters ◽  
Lower Mode ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon

This paper is an attempt to study the nonlinear vibration of a pre-stressed single-walled carbon nanotube (SWCNT) with water-filled and simply supported ends. A new analytical formula is obtained for the nonlinear model based on the simplified Donnell’s shell theory. The effects of internal fluid on the coupling vibration of the SWCNT–water system are discussed in detail. Furthermore, the influence of the different nanotube thicknesses and radiuses on the nonlinear vibration frequencies is investigated according to the shell theory. Numerical calculations are done to show the effectiveness of the proposed schemes. The results show that the nonlinear frequency grew with the increasing nonlinear parameters (radius and thickness of nanotube). In addition, it is shown that the influence of the nonlinear parameters is greater at the lower mode in comparison with the higher mode for the same nanotube thickness and radius.

Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using differential quadrature method

2015 ◽  
Vol 54 (6) ◽  
pp. 1061-1073 ◽  
Author(s):  
Hasan Rahimi Pour ◽  
Hossein Vossough ◽  
Mohammad Mehdi Heydari ◽  
Gholamhossein Beygipoor ◽  
Alireza Azimzadeh
Keyword(s):  
Carbon Nanotube ◽  
Nonlinear Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method

Accurate Solutions to Nonlinear Vibration of Single-Walled Carbon Nanotube via Homotopy Perturbation Method

2013 ◽  
Vol 662 ◽  
pp. 59-63
Author(s):  
Xin Mou Ma ◽  
Lie Zhen Chang
Keyword(s):  
Carbon Nanotube ◽  
Perturbation Method ◽  
Nonlinear Vibration ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Order Approximation ◽  
Accurate Solution ◽  
Single Walled Carbon Nanotube ◽  
Vibration Equation ◽  
Homotopy Perturbation

In this study, analytical solutions are obtained by homotopy perturbation method (HPM) for the nonlinear vibration equation of single-wall nanotube (SWNT). Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison of the result obtained by the HPM with exact solutions reveals that only the first or second order approximation of the HPM leads to higher accurate solution.

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