Nonlinear Oscillations of Gas Bubbles in Liquids: Steady State Solutions

The nonlinear oscillations of a spherical gas bubble in an incompressible, viscous liquid subject to the action of a sound field are investigated by means of an asymptotic method. Approximate analytical solutions for the steady?state oscillations are presented for the fundamental mode, for the first and second subharmonics, and for the first and second harmonics to second order in the expansion. These results are compared with some numerical ones and a very good agreement is found