Phononic thin plates with embedded acoustic black holes

We introduce a class of two-dimensional nonresonant single-phase phononic materials and investigate its peculiar dispersion characteristics. The material consists of a thin platelike structure with an embedded periodic lattice of acoustic black holes. The use of these periodic tapers allows achieving remarkable dispersion properties such as zero group velocity in the fundamental modes, negative group refraction index, birefraction, Dirac-like cones, and mode anisotropy. The dispersion properties are numerically investigated using both a three-dimensional supercell plane wave expansion method and finite element analysis. The effect on the dispersion and propagation characteristics of key geometric parameters of the black hole, such as the taper profile and the residual thickness, are also explored.