Acoustic passive cloaking using thin outer resonators

Abstract

We consider the propagation of acoustic waves in a 2D waveguide unbounded in one direction and containing a compact obstacle. The wavenumber is fixed so that only one mode can propagate. The goal of this work is to propose a method to cloak the obstacle. More precisely, we add to the geometry thin outer resonators of width $\epsilon$ and we explain how to choose their positions as well as their lengths to get a transmission coefficient approximately equal to one as if there were no obstacle. In the process we also investigate several related problems. In particular, we explain how to get zero transmission and how to design phase shifters. The approach is based on asymptotic analysis in presence of thin resonators. An essential point is that we work around resonance lengths of the resonators. This allows us to obtain effects of order one with geometrical perturbations of width $\epsilon$. Various numerical experiments illustrate the theory.

References in corpus (6)

• Acoustic cloaking theory
• Source amplitudes for active exterior cloaking
• Active Thermal Cloaking and Mimicking
• From zero transmission to trapped modes in waveguides
• Surface waves in a channel with thin tunnels and wells at the bottom: non-reflecting underwater tomography
• Design of an acoustic energy distributor using thin resonant slits

Cited by in corpus (1)

• Acoustic waveguide with a dissipative inclusion