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Periodic Solution for Strongly Nonlinear Oscillators by He’s New Amplitude–Frequency Relationship

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Abstract

This paper applies He’s new amplitude–frequency relationship recently established by He (Int J Appl Comput Math 3(2):1557–1560, 2017. doi:10.1007/s40819-016-0160-0) to study periodic solutions of strongly nonlinear systems with odd nonlinearities. Some examples are given to illustrate the effectiveness, ease and convenience of the method. In general, the results are valid for small as well as large oscillation amplitude. The method can be easily extended to other nonlinear systems with odd nonlinearities and can therefore be found widely applicable in engineering and other science. The method used in this paper can be applied directly to highly nonlinear problems without any discretization, linearization or additional requirements.

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Acknowledgements

The author would like to thank the anonymous referees for their constructive comments and suggestions that helped to improve the paper.

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  1. Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana-Cuajimalpa, Vasco de Quiroga 4871, Santa Fe, Cuajimalpa, 05300, Mexico City, Mexico

    O. González-Gaxiola

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González-Gaxiola, O. Periodic Solution for Strongly Nonlinear Oscillators by He’s New Amplitude–Frequency Relationship. Int. J. Appl. Comput. Math 3 (Suppl 1), 1249–1259 (2017). https://doi.org/10.1007/s40819-017-0414-5

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