Acoustic passive cloaking using thin outer resonators

• Published in: Zeitschrift für angewandte Mathematik und Physik Vol. 73; no. 3
• Main Authors: Chesnel, Lucas, Heleine, Jérémy, Nazarov, Sergei A.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-06-2022; Springer Nature B.V; Springer Verlag
• Subjects: Acoustic propagation; Acoustic waves; Analysis of PDEs; Barriers; Engineering; Mathematical Methods in Physics; Mathematics; Perturbation; Phase shifters; Resonators; Theoretical and Applied Mechanics; Wave propagation; Waveguides; Wavelengths; Complex resonance; Passive cloaking; Scattering coefficients; 35J05; 41A60; 35B40; Asymptotic analysis; Acoustic waveguide; Thin resonator; 78A40; 35Q60; 78M35; asymptotic analysis; thin resonator; scattering coefficients; passive cloaking; complex resonance
• ISSN: 0044-2275; 1420-9039
• DOI: 10.1007/s00033-022-01736-6

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
ε
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
ε
. Various numerical experiments illustrate the theory.