Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 956170, 11 pages
Research Article

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

I. Khatami,1 M. H. Pashai,1 and N. Tolou2

1Department of Mechanical Engineering, Mazandaran University, P.O. Box 484, Babol, Iran
2Department of Mechanical Engineering, Islamic Azad University - Amol Branch, P.O. Box 678, Amol, Iran

Received 28 March 2008; Revised 11 June 2008; Accepted 23 July 2008

Academic Editor: David Chelidze

Copyright © 2008 I. Khatami et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.