Mechanisms for Oscillations in Volume of Single Spherical Bubble Due to Sound Excitation in Water

Abstract

Mechanisms for the evolution of a single spherical bubble subjected to sound excitation in water are studied from the viewpoint of nonlinear dynamics. First, the shooting method is combined with a Poincaré map to obtain the fixed point for the case of forced oscillation in volume. Then, the stabilities are judged by Floquet theory and the bifurcation theorem. Moreover, the transitions of bubble oscillation in volume due to sound excitation in water are explained from the viewpoint of nonlinear dynamics in detail. The results show that with an increase in sound frequency, the period-1 oscillation becomes unstable, and oscillation behaves in a double-periodic manner, then a quasi-periodic manner, and finally chaotically. Additionally, with an increase of the amplitude of the sound pressure, the bubble eventually oscillates with chaos via a series of period-doubling bifurcations.