Rupin et al., Phys. Rev. Lett. (2014)

The setup of Fig.1 consists of a 6-mm-thick aluminum plate coupled with an ensemble of long aluminum rods which makes a locally resonant metamaterial. After a short vertical impulse is given to the plate using a shaker excited in the kHz regime, flexural A0 Lamb wave is generated having a typical wavelength of about 20 cm. The characterization of the reverberated wavefield inside the metamaterial is realized with a Laser Doppler Velocimeter pointing at a motorized mirror driven by a computer. Then, we do the sequential acquisition of a great number of impulse responses between the fixed location of the source and different points inside the metamaterial.

Based on a plane waves decomposition of the wavefield we obtain the dispersion relation given in Fig.2a. It exhibits three main propagation branches explained by the overlap of the polariton-like hybridizations caused by the three first compressional resonances of the rods which present very low quality factors (black line in Fig.2c). In addition, smaller effects are perceptible which are caused by the less efficient flexural resonances of the rods (grey line in Fig.2c). A very good match is observed with a numerical simulation performed on the unit cell of an equivalent periodic array with the Bloch periodic boundary conditions (dashed lines in Fig.2a). The evanescent part of the wavefield has also been determined (Fig.2b).