Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 327462, 20 pages
doi:10.1155/2009/327462
Research Article

Higher-Order Solutions of Coupled Systems Using the Parameter Expansion Method

S. S. Ganji,1 M. G. Sfahani,2 S. M. Modares Tonekaboni,3 A. K. Moosavi,2 and D. D. Ganji2

1Department of Civil and Transportation Engineering, Islamic Azad University, Science and Research Branch Campus, 4716695814 Tehran, Iran
2Department of Civil and Mechanical Engineering, Babol University of Technology, P.O. Box 484, 4714871167 Babol, Iran
3Department of Civil Engineering, Khajeh Nasir University of Technology, 1996715433 Tehran, Iran

Received 29 January 2009; Revised 27 April 2009; Accepted 7 June 2009

Academic Editor: Jerzy Warminski

Copyright © 2009 S. S. Ganji 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

We consider periodic solution for coupled systems of mass-spring. Three practical cases of these systems are explained and introduced. An analytical technique called Parameter Expansion Method (PEM) was applied to calculate approximations to the achieved nonlinear differential oscillation equations. Comparing with exact solutions, the first approximation to the frequency of oscillation produces tolerable error 3.14% as the maximum. By the second iteration the respective error became 1/5th, as it is 0.064%. So we conclude that the first approximation of PEM is so benefit when a quick answer is required, but the higher order approximation gives a convergent precise solution when an exact solution is required.