Cylindrical bubble dynamics in triple-frequency acoustic field

In this paper, the dynamic characteristics of the cylindrical bubbles under triple-frequency acoustic excitation are investigated theoretically. The analytical solution of the primary-superharmonic-subharmonic (PRI-SUPER-SUB) simultaneous resonance is obtained through the multi-scale method. Based on the analysis of the frequency response, the influencing mechanisms of the primary parameters (e.g., the total amplitude, amplitude ratio, liquid viscosity, polytropic exponent, and bubble equilibrium radius) on the resonance are investigated quantitatively. The main conclusions include: (1) The solution for the simultaneous resonance of the cylindrical bubble exhibits jumping and hysteresis phenomena in the vicinity of the resonance frequency. (2) As the total amplitude, amplitude ratio, and equilibrium radius increase, the response amplitude of the PRI-SUPER-SUB simultaneous resonance increases, while the influence of the viscosity is the opposite. (3) The regions dominated by the instability of the simultaneous resonance is significantly affected by the system parameters.