Low-frequency resonance of an oblate spheroidal cavity in a soft elastic medium

Axisymmetric monopole resonances of an oblate spheroidal cavity in a soft elastic medium are computed using both separation of variables and finite-element approaches. The resonances are obtained for compression wavelengths much longer than the cavity size and thus have a low-frequency character. Resonant frequencies for high-aspect-ratio oblate spheroids (either air-filled or evacuated) are found to be significantly lower than their spherical counterparts with equivalent volume. This finding contrasts with the case of an air bubble in water which features weak shape dependence. The results are relevant to the design of locally-resonant acoustic media using soft-lithography techniques with elastomers.