Applications of He's Homotopy Perturbation Method to Obtain Second-order Approximations of the Coupled Two-Degree-of-Freedom Systems

作者：Ganji S S^*; Ganji D D; Karimpour S; Babazadeh H

来源：International Journal of Nonlinear Sciences and Numerical Simulation, 2009, 10(3): 305-314.

DOI：10.1515/ijnsns.2009.10.3.305

• Coupled Two-Degree-of-Freedom (CTDOF)
• nonlinear oscillation
• Modified He's Homotopy Perturbation Method (MHHPM)

In this: paper we apply a Modified He's Homotopy Perturbation Method (MHHPM) as a-strong method to solve accurately higher-order approximate analytical Solutions of coupled two-degree-of-freedom (CTDOF), which is described with a system of two coupled strong non-linear differential equations. MHHPM is modified version of He's HPM by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution into the second-order linear differential equation. For the first approximation we achieve a high accuracy of Solutions with a maximal relative error less than 3.14% for small and large values of oscillation amplitude, while for the second iteration the fabulous relative error is 0.064%. It is predicted that MHHPM can be found widely applicable in engineering, which needs extremely accurate solutions,

• 出版日期2009-3