The attenuation of low-frequency sound has been a challenging task because the intrinsic dissipation of materials is inherently weak in this regime. Here we present a thin-film acoustic metamaterial, comprising an elastic membrane decorated with asymmetric rigid platelets that aims to totally absorb low-frequency airborne sound at selective resonance frequencies ranging from 100–1,000 Hz. Our samples can reach almost unity absorption at frequencies where the relevant sound wavelength in air is three orders of magnitude larger than the membrane thickness. At resonances, the flapping motion of the rigid platelets leads naturally to large elastic curvature energy density at their perimeter regions. As the flapping motions couple only minimally to the radiation modes, the overall energy density in the membrane can be two-to-three orders of magnitude larger than the incident wave energy density at low frequencies, forming in essence an open cavity.

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 ($\sim 200$ 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.

By using the $\stackrel{\rightharpoonup }{k}·\stackrel{\rightharpoonup }{p}$ method, we propose a first-principles theory to study the linear dispersions in phononic and photonic crystals. The theory reveals that only those linear dispersions created by doubly degenerate states can be described by a reduced Hamiltonian that can be mapped into the Dirac Hamiltonian and possess a Berry phase of $-\pi$. Linear dispersions created by triply degenerate states cannot be mapped into the Dirac Hamiltonian and carry no Berry phase, and, therefore should be called Dirac-like cones. Our theory is capable of predicting accurately the linear slopes of Dirac and Dirac-like cones at various symmetry points in a Brillouin zone, independent of frequency and lattice structure.

We show through rigorous derivation and experimental support that the dynamic effective mass density of an inhomogeneous mixture, used in the prediction of wave velocities in the long wavelength limit, can differ from the static version—the volume average of the component mass densities. The physical reason for this difference is explained. The dynamic mass density expression, first derived by Berryman more than two decades ago, is shown to give a closer correspondence between the acoustic and electromagnetic metamaterials by allowing for negative mass densities at frequencies around resonances.

By studying acoustic and electromagnetic wave transmission through a periodic array of subwavelength holes or slits with various channel lengths, we demonstrate both experimentally and theoretically that diffraction evanescent waves can play an important role in tuning the Fabry-Perot (FP) resonances. In particular, there can be total transmission peaks at wavelengths much below that of the Rayleigh-Wood limit, and FP resonances can occur for channel length $\sim 16\%$ thinner than the half wavelength. In addition, the FP resonance condition can be tuned via both the periodicity and area fraction of holes. As a function of the ratio between the periodicity and plate thickness, the FP resonance is smoothly linked to the surface-wave-like mode induced by the periodic structure factor.