14. Analytical periodic solution for solving nonlinear vibration equations
M. Bayat1, I. Pakar2, M. Bayat3
1Young Researchers and Elites Club, Science and Research Branch, Islamic Azad University, Tehran, Iran
2, 3Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
E-mail: firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
(Received 10 April 2013; accepted 7 June 2013)
Abstract: In this study a new kind of analytical methods called He’s variational approach method is applied to solve strong nonlinear vibration equations. The He’s variational approach method is very easy and contrary to the other conventional methods, only one iteration leads to high accuracy of the solutions for the whole range of initial amplitudes and does not demand small perturbation. Some examples are given to illustrate the effectiveness and convenience of the methodology. The Runge-Kutta’s (RK) algorithm was also implemented to achieve the numerical solutions for the examples. The results reveal that the variational approach method is very effective and simple. It is predicted that the VAM can find wide application in engineering problems, as indicated in following examples.
Keywords: variational approach method, nonlinear vibration, analytical methods.
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Cite this article
Bayat M., Pakar I., Bayat M. Analytical periodic solution for solving nonlinear vibration equations. Journal of Measurements in Engineering, Vol. 1, Issue 2, 2013, p. 86‑94.
Journal of Measurements in
Engineering. June 2013, Volume 1, Issue 2