Resonant phase lags of a Duffing oscillator

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:ν) and ultra-subharmonic (k:ν) 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 π/2 (phase quadrature) or 3π/4ν.

arXiv comment16 Pages, 8 figures

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Cited by in corpus (2)

• Tracking Superharmonic Resonances for Nonlinear Vibration of Conservative and Hysteretic Single Degree of Freedom Systems
• Efficient Model Reduction and Prediction of Superharmonic Resonances in Frictional and Hysteretic Systems