Sound insulation property of membrane-type acoustic metamaterials carrying different masses at adjacent cells

We have fabricated sonic crystals, based on the idea of localized resonant structures, that exhibit spectral gaps with a lattice constant two orders of magnitude smaller than the relevant wavelength. Disordered composites made from such localized resonant structures behave as a material with effective negative elastic constants and a total wave reflector within certain tunable sonic frequency ranges. A 2-centimeter slab of this composite material is shown to break the conventional mass-density law of sound transmission by one or more orders of magnitude at 400 hertz.

We present the experimental realization and theoretical understanding of a membrane-type acoustic metamaterial with very simple construct, capable of breaking the mass density law of sound attenuation in the 100-1000 Hz regime by a significant margin ( approximately 200 times). Owing to the membrane's weak elastic moduli, there can be low-frequency oscillation patterns even in a small elastic film with fixed boundaries defined by a rigid grid. The vibrational eigenfrequencies can be tuned by placing a small mass at the center of the membrane sample. Near-total reflection is achieved at a frequency between two eigenmodes where the in-plane average of normal displacement is zero. By using finite element simulations, negative dynamic mass is explicitly demonstrated at frequencies around the total reflection frequency. Excellent agreement between theory and experiment is obtained.

Metamaterials can exhibit electromagnetic and elastic characteristics beyond those found in nature. In this work, we present a design of elastic metamaterial that exhibits multiple resonances in its building blocks. Band structure calculations show two negative dispersion bands, of which one supports only compressional waves and thereby blurs the distinction between a fluid and a solid over a finite frequency regime, whereas the other displays 'super anisotropy' in which compressional waves and shear waves can propagate only along different directions. Such unusual characteristics, well explained by the effective medium theory, have no comparable analogue in conventional solids and may lead to novel applications.