Gas Bubble Oscillations in Non Simple-Harmonic Pressure Fields

The radial oscillations of a spherical gas bubble in an incompressible, viscous, liquid subject to a non simple-harmonic pressure field are considered. The analytical results concerning the bubble behavior in transient and steady-state oscillations are obtained by means of the multifrequency version of the Bogolyubov-Krylov averaging method. The analysis reveals the existence of combination resonances for which large bubble responses exist. These resonances are found in addition to the well known sub- and ultra-harmonic resonances characteristic of the monofrequency excitation. Moreover, simultaneous resonances which considerably influence the bubble behaviour are evidenced. The reported results seem very promising in dealing with the more general problem of bubbles in generig periodic pressure fields.