Department of Underwater Research, Swedish Defence Research Agency, SE-164 90 Stockholm, Sweden.
J Acoust Soc Am. 2012 Apr;131(4):2622-37. doi: 10.1121/1.3689852.
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.
水下声音反射的幅度可以通过包括三维（3-D）腔的橡胶涂层来减小，这些腔形成了双重周期性的衍射光栅。球形腔的单极共振增强了周围橡胶固体的吸收。本文研究了无限圆柱对应的共振。它出现在比具有相同半径的球体低得多的频率处，这表明包括圆柱形腔的更薄的消声涂层的可能性，这些圆柱形腔的轴在侧向形成具有单个周期的衍射光栅。由于轴向不变性，这实际上是一个 2-D 情况。使用层多次散射方法并包括不同尺寸的腔的后续涂层设计计算表明，涂层的反射减少了约三分之一，厚度却只有原来的三分之一。单极近似值仍考虑了腔之间的多次散射并捕获了基本物理现象，用于推进对反射减少的分析研究。导出了能量分解关系，并用于量化不同尺寸腔对入射声能的吸收。简要考虑了基于填充夹杂物和其他共振效应的涂层。再次，具有混合尺寸的圆柱的 2-D 替代方案给出了更薄的涂层。
