Application of amplitude-frequency formulation to nonlinear oscillation system of the motion of a rigid rod rocking back.

*(English)*Zbl 1387.34053Summary: The scope of this paper is evaluating an oscillation system with nonlinearities, using a periodic solution called amplitude-frequency formulation, such as the motion of a rigid rod rocking back. The approach proposes a choice to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. We are to compare the solutions results of this method with the exact ones in order to validate the approach and assess the accuracy of the solutions. This method has a distinguished feature, which makes it simple to use and agree with the exact solutions for various parameters. Moreover, it is perceived that with one-step iteration high accuracy of the solution will be achieved. We can apply the results of the solution to explain some of the practical physical problems.

##### MSC:

34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |

70E15 | Free motion of a rigid body |

70J10 | Modal analysis in linear vibration theory |

##### Keywords:

amplitude-frequency formulation (AFF); nonlinear oscillations; motion of a rigid rod rocking back; oscillation
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\textit{S. S. Ganji} et al., Math. Methods Appl. Sci. 33, No. 2, 157--166 (2010; Zbl 1387.34053)

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