Metamaterials for concealment and scattering reduction in acoustics and elasticity

Abstract

Avoiding detection from echolocation is one of the most interesting applications of acoustic metamaterials. Transformation Acoustics can be used to obtain perfect cloaking when a suitable mapping can be written, which is typically easy to find only for a restricted set of cases. In our work, we try to achieve scattering reduction and partial invisibility in a set of scenarios where practical feasibility is preventing perfect cloaking. First, we address the problem of underwater scattering reduction of elliptic obstacles, by applying suitable mapping defined in elliptical coordinates, which allow for practical realization and experimental testing of a non-axisymmetric, anisotropic pentamode near-cloak. Then, we approach the problem from a different perspective: specifically, we use PDE-constrained optimization aiming at cloaks obtained with isotropic materials only, which can be implemented with distributions of scatterers in the background fluid. The formulation of the optimization problem is done in such a way as to consider practical limits in the obtainable homogenized properties. In the same way of thinking i.e., isotropic materials are easier to implement than other exotic material distribution, we address elastic cloaking with isotropic materials, going back to Transformation Theories and exploiting conformal mapping, underlining the limits of applicability of such method to obtain cloak that works for Rayleigh waves. Finally, a different type of concealment can be conceived as being able to listen to what others say, without being listened to. This implies achieving nonreciprocal acoustic wave propagation. We derive the prescription for material properties that need to be implemented for non-reciprocal wave propagation of 2D cylindrical acoustic waves.