scholarly journals Accurate solutions to nonlinear vibration of cantilever beam via homotopy perturbation method

2011 ◽  
Vol 15 ◽  
pp. 4768-4773 ◽  
Author(s):  
Ma Xinmou ◽  
Chang Liezhen ◽  
Pan Yutian
Keyword(s):  
Perturbation Method ◽  
Nonlinear Vibration ◽  
Cantilever Beam ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation

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 Approximations for Large Deflection of a Cantilever Beam under a Terminal Follower Force and Nonlinear Pendulum

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
H. Vázquez-Leal ◽  
Y. Khan ◽  
A. L. Herrera-May ◽  
U. Filobello-Nino ◽  
A. Sarmiento-Reyes ◽  
...  
Keyword(s):  
Perturbation Method ◽  
Cantilever Beam ◽  
Homotopy Perturbation Method ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Approximate Solutions ◽  
Follower Force ◽  
Homotopy Perturbation ◽  
Solution Methods ◽  
Nonlinear Pendulum

In theoretical mechanics field, solution methods for nonlinear differential equations are very important because many problems are modelled using such equations. In particular, large deflection of a cantilever beam under a terminal follower force and nonlinear pendulum problem can be described by the same nonlinear differential equation. Therefore, in this work, we propose some approximate solutions for both problems using nonlinearities distribution homotopy perturbation method, homotopy perturbation method, and combinations with Laplace-Padé posttreatment. We will show the high accuracy of the proposed cantilever solutions, which are in good agreement with other reported solutions. Finally, for the pendulum case, the proposed approximation was useful to predict, accurately, the period for an angle up to179.99999999∘yielding a relative error of 0.01222747.

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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