The equations of motion of linear viscoelasticity (Kelvin–Voigt Model) in cylindrical coordinates are reduced to an axisymmetric plane-stress situation valid for short hollow cylinders. The analysis models the deformations and oscillations occurring in the annular region conceptually constructed around one of the holes in a multiperforated rubber sheet to be used as an underwater acoustic absorber. The eigenvalue problem for the ring’s natural frequencies is solved in two cases: first, when both rims of the ring are subjected to a stress boundary condition; second, when the inner rim (r=a) is stress free and the outer one (r=b) is fixed. For incompressible materials with Poisson’s ratio very close to 0.5, the first few eigen-wave-numbers are numerically computed and plotted in nondimensional form versus the b/a ratio, in both cases, and the resulting sets of curves are shown to be interlaced, the ones from the first case being below those of the second. The transient vibration problem for the displacement ur is solved by the Laplace-transform method in the first case only. The finding that the frequencies at which absorption is maxima are the resonant frequencies of the cavity, is verified. We show a simple technique to estimate the amount of absorption present at these eigenfrequencies, and the estimates reasonably check with experimental meaurements within the limitations of this model (i.e., below critical damping).
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G. C. Gaunaurd (1977) studied this question.