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http://dx.doi.org/10.12989/scs.2014.17.1.123

The analytic solution for parametrically excited oscillators of complex variable in nonlinear dynamic systems under harmonic loading  

Bayat, Mahdi (Department of Civil Engineering, College of Engineering, Mashhad Branch, Islamic Azad University)
Bayat, Mahmoud (Department of Civil Engineering, College of Engineering, Mashhad Branch, Islamic Azad University)
Pakar, Iman (Young Researchers and Elites Club, Mashhad Branch, Islamic Azad University)
Publication Information
Steel and Composite Structures / v.17, no.1, 2014 , pp. 123-131 More about this Journal
Abstract
In this paper we have considered the vibration of parametrically excited oscillator with strong cubic positive nonlinearity of complex variable in nonlinear dynamic systems with forcing based on Mathieu-Duffing equation. A new analytical approach called homotopy perturbation has been utilized to obtain the analytical solution for the problem. Runge-Kutta's algorithm is also presented as our numerical solution. Some comparisons between the results obtained by the homotopy perturbation method and Runge-Kutta algorithm are shown to show the accuracy of the proposed method. In has been indicated that the homotopy perturbation shows an excellent approximations comparing the numerical one.
Keywords
Homotopy Perturbation Method (HPM); Runge-Kutta Method (RKM); parametrically excited oscillator;
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Times Cited By KSCI : 4  (Citation Analysis)
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