Abstract
The exact theory of classical elasticity is used to calculate the response of an isotropic spherical shell to an acoustic mode of the fluid enclosed by the shell. The results are used to calculate the shifts of the acoustic resonance frequencies from the values which correspond to perfectly rigid shell walls. Acoustic modes with pressure proportional to Ynm (θ, φ) excite shell vibrations with the radial displacement also proportional to Ynm. The shell response depends upon the mode index n, the ratio of the shell diameters, Poisson’s ratio for the shell material, and a dimensionless frequency parameter. Numerical results for a useful range of acoustic frequencies are presented for radial (n=0) modes and for nonradial modes with mode indices n between 1 and 3. Numerical calculations of the shell resonance frequencies are presented for a wide range of shell thicknesses.
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