As building blocks of acoustic metamaterials, resonant scatterers have demonstrated their ability to modulate the effective fluid parameters, which subsequently possess extreme properties such as negative bulk modulus or negative mass density. Promising applications have been shown such as extraordinary absorption, focusing, and abnormal refraction for instance. However, acoustic waves can be further controlled in Willis materials by harnessing the coupling parameters. In this work, we derive the closed forms of the effective parameters from the transfer matrix in three asymmetric and reciprocal one-dimensional resonant configurations and exhibit the differences in terms of coupling coefficients. The way in which Willis coupling occurs in spatially asymmetric unit cells is highlighted. In addition, the analysis shows the absence of odd Willis coupling for reciprocal configurations. These effective parameters are validated against experimental and numerical results in the three configurations. This article paves the way of a novel physical understanding and engineering use of Willis acoustic materials.

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This paper examines the feasibility of cloaking an obstacle using Plate-type Acoustic Metamaterials (PAMs). We present two distinct strategies to cloak this obstacle, using either the near-zero-density regime of a periodic arrangement of plates or the acoustic doping phenomenon to achieve simultaneous zero-phase propagation and impedance matching. The strong limitations induced by viscothermal and viscoelastic losses that cannot be avoided in such a system are studied. A hiding zone is reported analytically, numerically, and experimentally. In contrast to cloaking, where zero-phase propagation must be accompanied by total transmission and zero reflection, the hiding configuration requires that the scattering properties of the hiding device must not be affected by the presence of the obstacle embedded in it. Contrary to cloaking, the hiding phenomenon is achievable even with a realistic PAM possessing unavoidable losses.