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 $\varepsilon$ 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 $\varepsilon$. Various numerical experiments illustrate the theory.
翻译:我们考虑将声波传播成2D波导,没有向一个方向,并包含一个紧凑的屏障。 波数是固定的,只有一种模式可以传播。 这项工作的目标是提出一个隐藏障碍的方法。 更准确地说, 我们增加宽度$\varepsilon的几何薄外部共振器, 我们解释如何选择其位置和长度, 以获得大约等于1的传输系数。 我们还调查了几个相关的问题。 特别是, 我们解释如何获得零传输, 以及如何设计相向转换器。 这种方法基于在薄共振器面前的无反应分析。 一个要点是, 我们围绕共振器的共振长度工作。 这使我们能够获得一个带有宽度$\varepsilon的几何干涉器的顺序效应。 各种数字实验可以说明这个理论。