Williams et al., Phys. Rev. B (2014)

Here, the experimental configuration described in Fig.1 is the one used in a previous paper (Phys. Rev.Lett., 2014). The metamaterial composed by long aluminum rods glued on a thin aluminum plate modifies the propagation of Lamb waves. The maps of the wavefields for 3 particular frequencies are given in the right panels of Fig.1. It shows three different regimes of propagation: sub-wavelength modes (top panel), forbidden frequency (middle panel), supra-wavelength mode (bottom panel).

This work propose to give an analytical expression for the dispersion relation experimentally determined (see Fig.2). To do so, we apply the scattering matrix formalism on a single rod attached to an uni-dimensional plate (beam). As a result we obtain an analytical expression for both the real part of the wavenumber (Fig.2a) and the imaginary part (Fig.2b).