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

The objective of this paper is to present an analytical investigation to analyze the vibration of parametrically excited oscillator with strong cubic negative nonlinearity based on Mathieu-Duffing equation. The analytic investigation was conducted by using He's homotopy-perturbation method (HPM...

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Bibliographic Details
Published inMathematical Problems in Engineering Vol. 2008; no. 1
Main Authors Khatami, I., Pashai, M. H., Tolou, N.
Format Journal Article
LanguageEnglish
Published New York Hindawi Limiteds 01.01.2008
Hindawi Publishing Corporation
Hindawi Limited
Subjects
Accuracy
Algorithms
Duffing equation
Exact solutions
Mathematical analysis
Mathematical models
Methods
Nonlinearity
Numerical analysis
Numerical methods
Oscillators
Perturbation methods
Runge-Kutta method
Studies
Vibration analysis
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Summary:The objective of this paper is to present an analytical investigation to analyze the vibration of parametrically excited oscillator with strong cubic negative nonlinearity based on Mathieu-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 approximate solution, has been shown graphically and compared with that of numerical solution. Afterward, the effects of variation of the parameters on the accuracy of the homotopy- perturbation method were studied.
ISSN:1024-123X
1563-5147
DOI:10.1155/2008/956170