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 (linearly) coupled nonlinear ordinary differential equations (ODEs). 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 ODE. Numerical data obtained by solving this 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...