Buy article PDF
The purchased file will be sent to you
via email after the payment is completed.
US$ 35
Steel and Composite Structures Volume 17, Number 1, July 2014 , pages 123-131 DOI: https://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 |
||
Mahdi Bayat, Mahmoud Bayat and Iman Pakar
|
||
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. | ||