Analytical Solutions for Free Vibration of Strongly Nonlinear Oscillators

Authors

M. Abul-Ez, Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, Egypt.Follow
G. M. Ismail, Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, Egypt.Follow
M. M. El-Moshneb, Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, Egypt.Follow

Abstract

In this paper, a nonlinear free vibration of strongly nonlinear oscillators is studied. To this end, we propose a novel technique using He’s frequency-amplitude formulation and He’s energy balance method called iteration perturbation procedure. A novel technique called iteration perturbation procedure and variational iteration method are presented to obtain the relationship between amplitude and angular frequency. The obtained results are compared with the numerical solution obtained by using the Runge–Kutta method and shown in graphs indicating the effectiveness and convenience of the analytical approximate solutions. These approaches are very effective and simple and with only one iteration leads to high accuracy of the solutions. It is predicted that those methods can be found wide applications in engineering problems, as indicated in this paper.

Recommended Citation

Abul-Ez, M.; M. Ismail, G.; and M. El-Moshneb, M. (2015) "Analytical Solutions for Free Vibration of Strongly Nonlinear Oscillators," Information Sciences Letters: Vol. 4 : Iss. 2 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol4/iss2/7