Nonlinear vibration of nonlocal four-variable graded plates with porosities implementing homotopy perturbation and Hamiltonian methods

2017 ◽  
Vol 229 (1) ◽  
pp. 343-362 ◽  
Author(s):  
Mohammad Reza Barati ◽  
Hossein Shahverdi
Keyword(s):  
Nonlinear Vibration ◽  
Homotopy Perturbation ◽  
Hamiltonian Methods

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.

scholarly journals Nonlinear vibration analysis of a rotor supported by magnetic bearings using homotopy perturbation method

2017 ◽  
Vol 6 (3) ◽  
pp. 223-232 ◽  
Author(s):  
Aboozar Heydari ◽  
Mina Mirparizi ◽  
Farshad Shakeriaski ◽  
Farhad Sheykh Samani ◽  
Mohamadreza Keshavarzi
Keyword(s):  
Perturbation Method ◽  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Homotopy Perturbation Method ◽  
Magnetic Bearings ◽  
Homotopy Perturbation

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.

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