Nonlinear Oscillations of Spherical Bubbles in Pressure Fields.

In the context of research on ship-propeller cavitation noise, an important role is played by formulas describing gas-bubble dynamic behavior in water. Nonlinear oscillations of a spherical gas bubble in an incompressible, viscous liquid subject to a sinusoidal pressure field are investigated by the multiscale perturbation method. Steady state response in the region of the main resonance is obtained at second order in the expansion. Analytical predictions show a fairly good agreement with numerical calculations. Results are promising for a study of the more general case in which pressure fields of arbitrary form can be considered, through a multifrequency excitation analysis.