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Analytical Solutions for Free Vibration of Strongly Nonlinear Oscillators |
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PP: 101-105 |
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Author(s) |
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M. Abul-Ez,
G. M. Ismail,
M. M. El-Moshneb,
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Abstract |
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| In this paper, a nonlinear free vibration of strongly nonlinear oscillators is studied. To this end, we propose a novel technique
using He’s frequency-amplitude formulation and He’s energy balance method called iteration perturbation procedure. A novel technique
called iteration perturbation procedure and variational iteration method are presented to obtain the relationship between amplitude and
angular frequency. The obtained results are compared with the numerical solution obtained by using the Runge–Kutta method and
shown in graphs indicating the effectiveness and convenience of the analytical approximate solutions. These approaches are very
effective and simple and with only one iteration leads to high accuracy of the solutions. It is predicted that those methods can be found
wide applications in engineering problems, as indicated in this paper. |
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