Determination of natural frequencies by coupled method of homotopy perturbation and variational method for strongly nonlinear oscillators

Journal Article · Tue Feb 15 00:00:00 EST 2011 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3534010· OSTI ID:21501279

Akbarzade, M; Langari, J ^[1]

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1. Department of Mechanical Engineering, Quchan Branch, Islamic Azad University, Quchan (Iran, Islamic Republic of)

In this paper a new approach combining the features of the homotopy concept with variational approach is proposed to find accurate analytical solutions for nonlinear oscillators with and without a fractional power restoring force. Since the first-order approximation leads to very accurate results, comparisons with other results are presented to show the effectiveness of this method. The validity of the method is independent of whether or not there exist small or large parameters in the considered nonlinear equations; the obtained results prove the validity and efficiency of the method, which can be easily extended to other strongly nonlinear problems. At the end we compare our procedure with the optimal homotopy perturbation method.

• OSTI ID: 21501279
• Journal Information: Journal of Mathematical Physics, Vol. 52, Issue 2; Other Information: DOI: 10.1063/1.3534010; (c) 2011 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ANALYTICAL SOLUTION
APPROXIMATIONS
COMPARATIVE EVALUATIONS
DIFFERENTIAL EQUATIONS
HARMONIC OSCILLATORS
NONLINEAR PROBLEMS
OSCILLATORS
PERTURBATION THEORY
VARIATIONAL METHODS
CALCULATION METHODS
ELECTRONIC EQUIPMENT
EQUATIONS
EQUIPMENT
EVALUATION
MATHEMATICAL SOLUTIONS