Scattering reduction of an acoustically hard cylinder covered with layered pentamode metamaterials

Transformational acoustics offers the theoretical possibility of cloaking obstacles within fluids, provided metamaterials having continuously varying bulk moduli and densities can be found or constructed. Realistically, materials with the proper, continuously varying anisotropies do not presently exist. However, discretely layered cloaks having constant material parameters within each layer may be a viable alternative in practice. The present work considers a range of cloaks, from those comprised of fluid layers that are isotropic in bulk moduli with anisotropic density (inertial cloaks) to those having anisotropic bulk moduli and isotropic density (pentamode cloaks). In this paper an analytical solution is obtained for the case of plane wave scattering from a submerged rigid cylinder covered with a multilayered cylindrical cloak composed of discrete anisotropic fluid layers. An investigation of the parameter space defining such cloaks is undertaken with the goal of minimizing the far-field scattered pressure, using layer constituent anisotropic properties (density and bulk modulus) constrained to lie within reasonable ranges relative to those of water.