Anechoic coatings obtained from two- and three-dimensional monopole resonance diffraction gratings

Abstract

Underwater sound reflections can be reduced in magnitude by a rubber coating including three-dimensional (3-D) cavities forming a doubly periodic diffraction grating. A monopole resonance for sphere-like cavities enhances absorption in the surrounding rubber solid. A corresponding resonance for an infinite cylinder is studied in the present paper. Appearing at a considerably lower frequency than for a sphere with the same radius, it suggests the possibility of much thinner anechoic coatings including cylindrical cavities, with axes in a lateral direction, forming a diffraction grating with a single period. This is effectively a 2-D case, because of invariance in the axial direction. Subsequent coating design computations, using the layer-multiple-scattering method and including cavities of different sizes, show improved reflection reduction with coatings only about one third as thick. Still accounting for multiple scattering among the cavities and capturing the essential physics, the monopole approximation is applied to advance the analytic study of the reflection reduction. An energy decomposition relation is derived and used to quantify the absorption of the incident sound energy by cavities of different sizes. Coatings based on filled inclusions and other resonance effects are briefly considered. Again, the 2-D alternative with cylinders of mixed sizes gives thinner coatings.