Comparative Vibration Analysis of a Parametrically Nonlinear Excited Oscillator Using HPM and Numerical Method | Zendy

I. Khatami | Zendy; M. H. Pashai | Zendy; N. Tolou | Zendy

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Comparative Vibration Analysis of a Parametrically Nonlinear Excited Oscillator Using HPM and Numerical Method

Author(s) -

I. Khatami,

M. H. Pashai,

N. Tolou

Publication year - 2008

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2008/956170

Subject(s) - duffing equation , homotopy perturbation method , homotopy analysis method , mathematics , nonlinear system , vibration , perturbation (astronomy) , mathematical analysis , poincaré–lindstedt method , numerical analysis , homotopy , physics , singular perturbation , quantum mechanics , pure mathematics

The objective of this paper is to present an analytical investigation to analyze thevibration of parametrically excited oscillator with strong cubic negative nonlinearity based onMathieu-Duffing equation. The analytic investigation was conducted by using He's homotopy-perturbation method (HPM). In order to obtain the analytical solution of Mathieu-Duffing equation, homotopy-perturbation method has been utilized. The Runge-Kutta's (RK) algorithm was used to solve the governing equation via numerical solution. Finally, to demonstrate the validity of the proposed method, the response of the oscillator, which was obtained from approximatesolution, has been shown graphically and compared with that of numerical solution. Afterward, theeffects of variation of the parameters on the accuracy of the homotopy-perturbation method were studied

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