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A new frequency domain representation and analysis for subharmonic oscillation

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Abstract

For a weakly nonlinear oscillator, the frequency domain Volterra kernels, often called the generalized frequency response functions, can provide accurate analysis of the response in terms of amplitudes and frequencies, in a transparent algebraic way. However, a Volterra series representation based analysis will become void for nonlinear oscillators that exhibit subharmonics, and the problem of finding a solution in this situation has mainly been treated by traditional analytical approximation methods. In this paper, a novel method is developed, by introducing a frequency domain subharmonic kernel representation for subharmonic systems subject to a single tone excitation frequency, to allow the advantages and the benefits associated with the traditional frequency domain representations to be applied to severely nonlinear systems that exhibit subharmonic behavior.

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Acknowledgements

The authors gratefully acknowledge that this work was supported by the Engineering and Physical Sciences Research Council (EPSRC) UK, and a European Research Council Advanced Investigator Award.

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Authors and Affiliations

  1. Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, S1 3JD, UK

    L. M. Li & S. A. Billings

  2. School of Mechanical Engineering and Automation, HIT Campus of ShenZhen University Town, Xili, ShenZhen, China

    L. M. Li

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  1. L. M. Li
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  2. S. A. Billings
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Correspondence to S. A. Billings.

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Li, L.M., Billings, S.A. A new frequency domain representation and analysis for subharmonic oscillation. Nonlinear Dyn 70, 1485–1497 (2012). https://doi.org/10.1007/s11071-012-0549-1

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  • DOI: https://doi.org/10.1007/s11071-012-0549-1

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