Effective impedance of a locally resonant metasurface

We study here a mesoscopic metasurface made of a randomly distributed set of long vertical metallic rods attached to a thin elastic plate. The A(0) Lamb wave propagation is strongly affected by the local change in apparent stiffness of the plate induced by the low-quality factor resonance of the rods. At the resonance, the plate-plus-rods system is allowed to move freely, and plate waves can penetrate into the metamaterial. At the antiresonance, the plate behaves in terms of waves as if it was clamped by the rods in the metamaterial region, which induces large-frequency band gaps. Between the resonant and antiresonant frequencies, the continuous change in effective rigidity results in a continuous change in reflectivity. In the present paper, we aim at measuring the corresponding complex impedance of the metasurface in terms of amplitude and phase. Experimental data are presented to estimate the effective impedance of a locally resonant metasurface, in agreement with theoretical prediction and numerical simulation.