Non-linear bubbly Helmholtz resonator
Résumé
Microbubble clouds greatly affect the acoustic behaviour of systems such as liquid-filled Helmholtz resonators. Gas microbubbles change the resonator’s behaviour from quasi-linear to mostly non-linear, together with the appearance of hysteretic phenomena and desymmetrisation of the temporal response or a softening effect with a drop in the resonance frequencies with increasing excitation amplitudes. The aim of this study is to model the non-linear behaviour of a diphasic Helmholtz resonator filled with water containing air microbubbles. The microbubble cloud is therefore modelled with a “damped-mass-spring” second-order equation. The impact of the two phases is accounted for by considering both an equivalent stiffness and an equivalent damping value. The model is then compared to experimental data, which showed its ability to reproduce both linear and non-linear behaviour.
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