Destructive frequency of oblate spheroidal air-balloon for suppression of propeller cavitation induced hull excitation

The air-balloon can effectively neutralize hull excitations induced by the propeller cavitation. For the design, it is essential to derive the destructive frequency of an oblate spheroidal air-bubble, which is elaborated on in this paper. Beginning with the exact modal-series solution proposed by Yeh [Ann. Phys. 468, 53–61 (1964)], an approximated form of the scattered pressure is set up by assuming that the acoustic wavelength is much larger than the size of the balloon in the low frequency ranges. An algebraic formula for the destructive frequency can then be written as a function of the resonance frequency and a spatial variable. It is well known that the resonance frequency of a deformed bubble is higher than that of an ideal spherical one with the same volume. In addition to this, the current investigation puts an emphasis on the fact that asphericity induces a more severe shift of the destructive frequency than the resonance frequency, and that its effect needs to be reflected in the balloon design.