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Amplitude-Frequency Relationship for Conservative Nonlinear Oscillators with Odd Nonlinearities

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Abstract

This paper studies a conservative nonlinear oscillator with odd nonlinearities, u\(^{\prime \prime }+f(u)=0\), the square of its frequency is f\(^{\prime }(\hbox {u}_\mathrm{i})\), where \(\hbox {u}_\mathrm{i}\) is a location point. A criterion on how to choose a location point is given. Dufffing equation is used as an example to show the accuracy of the prediction.

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References

  1. He, J.H.: An improved amplitude-frequency formulation for nonlinear oscillators. Int. J. Nonl. Sci. Num. 9(2), 211–212 (2008)

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  2. He, J.H.: Max-min approach to nonlinear oscillators. Int. J. Nonl. Sci. Num. 9(2), 207–210 (2008)

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  3. He, J.H.: Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20, 1141–1199 (2006)

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  4. He, J.H.: Nonperturbative methods for strongly nonlinear problems. dissertation.de-Verlag im Internet GmbH (2006)

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Acknowledgments

The work is supported by PAPD (A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions), “Six Talent Peak” of Jiangsu Province (ZBZZ-035).

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Correspondence to Ji-Huan He.

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He, JH. Amplitude-Frequency Relationship for Conservative Nonlinear Oscillators with Odd Nonlinearities. Int. J. Appl. Comput. Math 3, 1557–1560 (2017). https://doi.org/10.1007/s40819-016-0160-0

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  • DOI: https://doi.org/10.1007/s40819-016-0160-0

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