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Mathematical Problems in Engineering
Volume 2009, Article ID 450862, 9 pages
Research Article

Higher-Order Approximate Periodic Solutions of a Nonlinear Oscillator with Discontinuity by Variational Approach

1Faculty of Aeronautics and Astronautics, Istanbul Technical University, Maslak 34469, Istanbul, Turkey
2Faculty of Science and Letters, Istanbul Technical University, Maslak 34469, Istanbul, Turkey

Received 16 October 2008; Revised 12 March 2009; Accepted 14 May 2009

Academic Editor: Ekaterina Pavlovskaia

Copyright © 2009 M. Orhan Kaya 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.


He's variational approach is modified for nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(u). Three levels of approximation have been used. We obtained 1.6% relative error for the first approximate period, 0.3% relative error for the second-order approximate period. The third approximate solution has the accuracy as high as 0.1%.