Purpose
The purpose of this paper is to present an analytical technique, based on the He’s energy balance method (an improved version recently presented by Khan et al.), to obtain the approximate solution of quadratic nonlinear oscillator (QNO).
Design/methodology/approach
This oscillator (QNO) is used as a mathematical model of the human eardrum oscillation.
Findings
It has been shown that the results by the present technique are very close to the numerical solution.
Originality/value
The results obtained in this paper are compared with those obtained by Hu (harmonic balance method) and Khan et al. The result shows that the method is more accurate and effective than harmonic balance as well as improved energy balance methods.
Some strongly nonlinear oscillators have been investigated with the help of combined modified Lindstedt–Poincare and homotopy perturbation methods. The solutions are more accurate than those obtained by the modified Lindstedt–Poincare method. Moreover, the determination of solutions is simpler than usual homotopy perturbation methods. Some similarities and dissimilarities between the present method and other existing methods have also been discussed.
Combining the general Struble's technique and homotopy perturbation method, an analytical technique has been presented to determine approximate solutions of strongly nonlinear differential systems with severe damping effect in the presence of an external force. The method is illustrated by examples. The approximate solutions show a good coincidence with corresponding numerical solution (considered to be exact). Moreover, it provides better result than other existing solutions (derived by several analytical methods). Ó 2015 Production and hosting by Elsevier B.V. on behalf of Ain Shams University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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