Simultaneous resonance characteristics of cylindrical bubbles under dual-frequency acoustic excitation based on singular-perturbation theory

The simultaneous resonance patterns and dynamic attributes of cylindrical bubbles subjected to dual-frequency acoustic excitation are explored in this article. Specifically, analytical models and local stability analysis are constructed for different types of simultaneous resonance under dual-frequency acoustic excitation. Based on the frequency response curve, the mechanisms whereby the core parameters in dual-frequency excitation influence the resonant dynamic characteristics are then explored. Combined with the Lyapunov exponent and amplitude, frequency, and phase, bifurcation diagrams are illustrated for determining the global stability of the cylindrical bubble dual-frequency resonance system. The conclusions from this research are given as follows: (1) Under dual-frequency acoustic excitation, the simultaneous resonance type can be subdivided into three categories, namely, primary–superharmonic, primary–subharmonic, and superharmonic–subharmonic simultaneous resonances. These dual-frequency resonance types exhibit unique and significant dynamic characteristics. (2) Increasing the total amplitude of dual-frequency acoustic excitation significantly enhances the maximum value of the dual-frequency resonance and the vulnerability to instabilities. The effect of the bubble balance radius is similar to that of the total amplitude. Higher values of the nonlinear coefficient reduce the maximum value of the resonance and increase the likelihood of instability. (3) The total amplitude of dual-frequency acoustic excitation is a key factor affecting the stability of bubbles. As the total amplitude increases, the bubble oscillation gradually transforms from periodic to chaotic.