Table of Contents
International Journal of Computational Mathematics
Volume 2014, Article ID 939623, 7 pages
http://dx.doi.org/10.1155/2014/939623
Research Article

Approximate Periodic Solution for the Nonlinear Helmholtz-Duffing Oscillator via Analytical Approaches

1School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
2Department of Mechanical Engineering, Amirkabir University of Technology, Hafez Avenue, Tehran 15914, Iran

Received 1 June 2014; Accepted 17 September 2014; Published 29 September 2014

Academic Editor: Anh-Huy Phan

Copyright © 2014 A. Mirzabeigy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The conservative Helmholtz-Duffing oscillator is analyzed by means of three analytical techniques. The max-min, second-order of the Hamiltonian, and the global error minimization approaches are applied to achieve natural frequencies. The obtained results are compared with the homotopy perturbation method and numerical solutions. The results show that second-order of the global error minimization method is very accurate, so it can be widely applicable in engineering problems.