Abstract
Acoustic cloaking for the suppression of backscattering inside ducts is proposed in the audible range where plane waves are curved around the object using the surface modes of the liner. It is numerically shown that a slowly varying resonant liner (e.g. based on an array of tubes) creates a zone of silence in which an object of arbitrary shape can be acoustically hidden for a wide range of frequencies. And then, a resonant liner has deflecting properties without reflection of the wavefront, which are close to an ideal invisibility cloak. This kind of cloaking is effective in a wide frequency band and the cloaking band is a function of the impedance and height of the obstacle relative to the conduit. For smooth shaped obstacles, there is an ability of the object to help hide itself, which increases the cloaking frequency band (self-cloaking). Dispersion effects lead to slow sounds and distortion of the wave phase.
Highlights
Hiding an obstacle from the scattering of electromagnetic, acoustic or elastic waves has recently been a subject of particular interest because of its promising applications[1,2,3,4,5]
We propose to use for the first time a similar concept in acoustics
They act according to two distinct principles: the absorption of acoustic energy by visco-thermal effects and the scattering of acoustic waves by variations in the properties or geometry of the material that can occur even with non-dissipative liners[16]
Summary
We consider the sound propagation in a two dimensional channel, see Fig. 1. If the admittance is positive and, is slowly varying compared to the sound wavelength, the local value of α increases progressively as Y increases It means that the wave is more and more concentrated against the wall, see Fig. 2(b). With admittance, |R| is maximized by 2|R∞|, plotted in green on Fig. 3(a,d), where R∞ is the reflection coefficient of an ascending step in presence of a uniform admittance on the upper wall that can be computed by a multimodal method. The upper frequency of the cloaking band is given by the tube resonance (kb = π/2) This example shows that any object located in the shadow zone produces a small reflection on a broad frequency band even if this object covers the substantial surface of the shadow zone. An envelope of |R| near and in the cloaking band can be computed from the admittance and from the maximum height of the object
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