Sound absorption by viscoelastic coatings with periodically distributed cavities

Thin rubber layers with air-filled cavities can be used as anechoic submarine coatings. Normally incident sonar energy is redistributed in the lateral direction and absorbed. In this paper, the anechoic effect is studied theoretically and numerically by adapting techniques used in electron scattering and band-gap computations for photonic and phononic crystals. Reflection and transmission matrices are computed recursively, from basic ones for layers containing periodic arrays of spherical cavities. A method to locate zeroes of analytical functions is applied to prove the existence of, and to specify, thin coatings with vanishing reflectance at isolated frequencies. Coatings much thinner than quarter-wavelength ones are found. Most of the absorption loss takes place close to the cavities and scattering of compressional spherically symmetric waves is important. The viscoelastic shear-wave properties of the rubber are crucial for generating this loss. The requirements for vanishing reflectance are specified using a simplified model with normal plane waves and spherically symmetric waves, that includes effects of multiple scattering among the cavities. An energy relation is derived, relating the anelastic loss in the rubber coating to loss by monopole resonance scattering from isolated cavities. The noticeable effects of multiple scattering are incorporated by a modulating factor.