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Frequency analysis of nonlinear oscillations via the global error minimization

Frequency analysis of nonlinear oscillations via the global error minimization AbstractThe capacity and effectiveness of a modified variational approach, namely global error minimization (GEM) is illustrated in this study. For this purpose, the free oscillations of a rod rocking on a cylindrical surface and the Duffing-harmonic oscillator are treated. In order to validate and exhibit the merit of the method, the obtained result is compared with both of the exact frequency and the outcome of other well-known analytical methods. The corollary reveals that the first order approximation leads to an acceptable relative error, specially for large initial conditions. The procedure can be promisingly exerted to the conservative nonlinear problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Engineering de Gruyter

Frequency analysis of nonlinear oscillations via the global error minimization

Kalami Yazdi, M; Hosseini Tehrani, P
Nonlinear Engineering , Volume 5 (2): 6 – Jun 1, 2016
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Publisher
de Gruyter
Copyright
© 2016 Walter de Gruyter GmbH, Berlin/Boston
ISSN
2192-8029
eISSN
2192-8029
DOI
10.1515/nleng-2015-0036
Publisher site
See Article on Publisher Site

Abstract

AbstractThe capacity and effectiveness of a modified variational approach, namely global error minimization (GEM) is illustrated in this study. For this purpose, the free oscillations of a rod rocking on a cylindrical surface and the Duffing-harmonic oscillator are treated. In order to validate and exhibit the merit of the method, the obtained result is compared with both of the exact frequency and the outcome of other well-known analytical methods. The corollary reveals that the first order approximation leads to an acceptable relative error, specially for large initial conditions. The procedure can be promisingly exerted to the conservative nonlinear problems.

Journal

Nonlinear Engineering – de Gruyter

Published: Jun 1, 2016

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