Wave beaming and diffraction in quasicrystalline elastic metamaterial plates

Abstract

In this paper, we present evidence of directional wave behavior, i.e., beaming and diffraction, along high-order rotational symmetries of quasicrystalline elastic metamaterial plates. These structures are obtained by placing pillars on an elastic plate following a particular rotational symmetry arrangement, such as eightfold and tenfold rotational symmetries, as enforced by a design procedure in reciprocal space. We estimate the dispersion properties of the waves propagating in the plates through Fourier transformation of transient wave fields. The procedure identifies, both numerically and experimentally, the existence of anisotropic bands characterized by high-energy density at isolated zones in reciprocal space that follow their higher order rotational symmetry. Specific directional behavior is showcased at the identified frequency bands, such as wave beaming (predicted in simulations and confirmed experimentally) and diffraction (exemplified only with numerical results). This paper expands the wave directionality phenomena beyond the symmetries of periodic configurations (e.g., fourfold and sixfold), and opens possibilities for applications involving the unusual high-order wave features of the quasicrystals (e.g., eightfold and tenfold) such as superior guiding, focusing, sensing, and imaging.