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Steel and Composite Structures
  Volume 17, Number 1, July 2014 , pages 123-131

The analytic solution for parametrically excited oscillators of complex variable in nonlinear dynamic systems under harmonic loading
Mahdi Bayat, Mahmoud Bayat and Iman Pakar

    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.
Key Words
    Homotopy Perturbation Method (HPM); Runge-Kutta Method (RKM); parametrically excited oscillator
(1) Mahdi Bayat, Mahmoud Bayat:
Department of Civil Engineering, College of Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran;
(2) Iman Pakar:
Young Researchers and Elites Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran.

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