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.

Homotopy Perturbation Method for Analysis Nonlinear Vibration of Double-Walled Carbon Nanotubes

2013 ◽  
Vol 702 ◽  
pp. 186-190
Author(s):  
Lie Zhen Chang ◽  
Yu Tian Pan ◽  
Xin Mou Ma
Keyword(s):  
Carbon Nanotubes ◽  
Perturbation Method ◽  
Nonlinear Vibration ◽  
Homotopy Perturbation Method ◽  
Order Approximation ◽  
Accurate Solution ◽  
Homotopy Perturbation ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
Approximately Analytical Solution

To obtain the approximately analytical solution of double-walled carbon nanotubes (DWNTs) nonlinear vibration. In this study, homotopy perturbation method (HPM) was used to solve nonlinear vibration equation of DWNTs. 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.

Application of homotopy perturbation method for dynamic analysis of nanotubes delivering nanoparticles

2020 ◽  
pp. 107754632093347
Author(s):  
Beytollah Rezapour ◽  
Mohammad Ali Fariborzi Araghi ◽  
Hector Vázquez-Leal
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Order Approximation ◽  
Beam Theory ◽  
Nonlinear Frequency ◽  
Inertial Forces ◽  
Homotopy Perturbation ◽  
Vibration Behavior ◽  
Wide Range ◽  
Euler Bernoulli Beam

Because of the importance of the analytical study of the vibration behavior of nanotubes delivering nanoparticles, in this study, the transverse vibration of these systems has been studied by analytical approach based on the homotopy perturbation method. The nonlocal Euler–Bernoulli beam theory is used for derivation of the equation of motion. The interaction between nanoparticle and the inner wall of nanotube has been modeled by using van der Waals forces and considering the effects of inertial forces caused by centrifugal and Coriolis acceleration components of nanoparticles. After evaluation of the implemented analytical method by numerical results, it is revealed that the obtained second-order approximation response gives high accurate vibration behavior of these systems for a wide range of parameters. As well, these results show that inertial forces caused by motion of nanoparticle increase vibration amplitude of nanotube and change nonlinear frequency of the system.

Homotopy Perturbation Method for Nonlinear Vibration Analysis of Functionally Graded Plate

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Ali A. Yazdi
Keyword(s):  
Perturbation Method ◽  
Material Properties ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Order Approximation ◽  
Oscillation Amplitude ◽  
Functionally Graded ◽  
Homotopy Perturbation ◽  
Graded Material ◽  
First Order Approximation

In this paper, the Homotopy perturbation method (HPM) is used to analysis the geometrically nonlinear vibrations of thin rectangular laminated functionally graded material (FGM) plates. The Von Karman's strain-displacement relations have been employed to model structural nonlinearity of the system. The material properties of the plate are assumed to be graded continuously in direction of thickness. The effects of initial deflection, aspect ratio and material properties are investigated. Based on the results of this study, the first order approximation of the HPM leads to highly accurate solutions for geometrically nonlinearity vibration of FGM plates. Moreover, HPM in comparison with other traditional analytical methods (e.g., perturbation methods) has excellent accuracy for the whole range of oscillation amplitude and initial conditions.

scholarly journals Hybridization of homotopy perturbation method and Laplace transformation for the partial differential equations

2017 ◽  
Vol 21 (4) ◽  
pp. 1843-1846 ◽  
Author(s):  
Zhen-Jiang Liu ◽  
Magaji Adamu ◽  
Enoch Suleiman ◽  
Ji-Huan He
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Analytical Solutions ◽  
Laplace Transformation ◽  
Homotopy Perturbation Method ◽  
Solution Process ◽  
Initial Approximation ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Linear Differential

Homotopy perturbation method is combined with Laplace transformation to obtain approximate analytical solutions of non-linear differential equations. An example is given to elucidate the solution process and confirm reliability of the method. The result indicates superiority of the method over the conventional homotopy perturbation method due its flexibility in choosing its initial approximation.

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