A new analytical technique based on harmonic balance method to determine approximate periods for Duffing-harmonic oscillator
The Duffing-harmonic oscillator is a common model for nonlinear phenomena in science and engineering. In this paper, a new analytical technique has been presented to determine approximate periods of a strongly nonlinear Duffing-harmonic oscillator. Generally, a set of difficult nonlinear algebraic...
| Main Authors: | , |
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| Format: | Article |
| Language: | English English |
| Published: |
Published by Elsevier
2015
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/44796/ http://irep.iium.edu.my/44796/ http://irep.iium.edu.my/44796/ http://irep.iium.edu.my/44796/1/A_new_analytical_technique_based_on_harmonic_balance_method_to_determine_approximate_periods_for_Duffing-harmonic_oscillator.pdf http://irep.iium.edu.my/44796/4/44796__WOS_and_SCOPUS.pdf |
| Summary: | The Duffing-harmonic oscillator is a common model for nonlinear phenomena in science and engineering. In this paper, a new analytical technique has been presented to determine approximate periods of a strongly nonlinear Duffing-harmonic oscillator. Generally, a set of difficult
nonlinear algebraic equations appear when harmonic balance method is imposed. The power series solutions of these equations are invalid. The proposed idea avoids this limitation and the necessity of numerically solving such nonlinear algebraic equations with very complex nonlinearities. In this technique, different parameters for the same nonlinear problems are found, for which the power
series solution yields desired results. Besides a suitable truncation formula is found in which the solution measures better results than existing solutions. It is remarkable that this procedure is simple and takes less computational effort for determining second and higher order periods of oscillation for such nonlinear problems and shows a good agreement compared with the exact ones. |
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