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Steel and Composite Structures Volume 17, Number 1, July 2014 , pages 123-131 DOI: https://doi.org/10.12989/scs.2014.17.1.123 |
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The analytic solution for parametrically excited oscillators of complex variable in nonlinear dynamic systems under harmonic loading |
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Mahdi Bayat, Mahmoud Bayat and Iman Pakar
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| 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. | ||
| Key Words | ||
| Homotopy Perturbation Method (HPM); Runge-Kutta Method (RKM); parametrically excited oscillator | ||
| Address | ||
| (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. | ||