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arXiv · 2202.07556

Resonant phase lags of a Duffing oscillator

Martin Volvert·Gaetan Kerschen
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Abstract

This paper revisits the resonant behavior of a harmonically-forced Duffing oscillator with a specific attention to phase resonance and to its relation with amplitude resonance. To this end, the different families of resonances, namely primary (1:1), superharmonic (k:1), subharmonic (1:{\nu}) and ultra-subharmonic (k:{\nu}) resonances are carefully studied using first and higher-order averaging. When the phase lag is calculated between the k-th harmonic of the displacement and the harmonic forcing, this study evidences that phase resonance occurs when the phase lag is equal to either {\pi}/2 (phase quadrature) or 3{\pi}/4{\nu}.

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Martin Volvert, Gaetan Kerschen. 2022-02-15. Resonant phase lags of a Duffing oscillator. https://doi.org/10.1016/j.ijnonlinmec.2022.104150

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