Dual-frequency excited combination resonance and global stability of an oscillating cylindrical bubble

Based on the multi-scale method and Lyapunov stability theory, the second-order analytical model of combination resonance under dual-frequency acoustic excitation of an oscillating cylindrical bubble is established. The nonlinear dynamic characteristics of the additive combination resonance and the subtractive combination resonance are explored by analyzing the frequency response curve and global stability. The primary findings are given as follows: (1) the combination resonance exhibits complex dynamic characteristics, which are manifested in the frequency response curve as multiple response peaks and unstable regions. (2) The response peak of the additive combination resonance consists of a single resonance peak on the left and a small-amplitude double peak on the right. The response amplitude is highly sensitive to changes in core parameters, and the changes at the top of the response peak are obvious. (3) The response peak of the subtractive combination resonance is composed of a large-amplitude double-peak resonance on the left and a small-amplitude single-peak resonance on the right. When the frequency is relatively high, three discontinuous unstable regions will appear in the frequency response curve.