Negative effective mass density of acoustic metamaterial plate decorated with low frequency resonant pillars

Abstract

We investigate the elastic wave dispersion by a phononic metamaterial plate containing low frequency resonator stubs arranged periodically over the plate. We show that this system not only provides stop bands for wavelengths much larger than the periodicity but also displays negative behavior of its effective mass density under the homogenization assumption. A numerical method is used to calculate the plate's effective dynamic mass density as function of the frequency where the metamaterial is considered as homogeneous plate for these large wavelengths. Strong anisotropy of the effective mass density matrix is observed around the resonance frequencies where the gaps are opened. In these regions, we demonstrate that the effective matrix density components take negative values. For each of these components, the negative behavior is studied by taking into account the polarization of the involved resonant modes as well as their associated partial band gaps opened for each specific Lamb symmetry modes. We found that coupling between Lamb waves and resonant modes strongly affects the effective density of the whole plate especially in the coupling frequency regions of the gaps.