Coupled nonlinear oscillations of microbubbles

Abstract

The coupling effects on the acoustic signature from nonlinear oscillations of a group of microbubbles is investigated. In general, exploring this phenomenon would require solving a set of (linearly) coupled nonlinear ordinary differential equations (\lowercase {ODE}s). However, assuming that the initial conditions of all bubbles are identical and that all bubbles are equi-distant from each other simplifies the governing equations to just a single \lowercase {ODE}. Numerical data obtained by solving this \lowercase {ODE} is used to investigate the effects of bubble population size on the subharmonics and ultraharmonics of the system. As the number of bubbles is increased, the natural frequency and the damping of the system decreases. There is a slight shift in the frequencies at which the maximum bubble oscillation occur. The amplitude of oscillations near the main resonance are significantly reduced as the number of bubble increases.