Phononic crystals with archimedean-like tiling: band structure and the transformation of sound

In this study, we investigate acoustic wave propagation in 3 D phononic crystal (PnC) slabs wherein scatterers have different cross sections by using the finite-element method. The PnC consists of scatterers embedded in the host material arranged in a square lattice and honeycomb lattice in different patterns (bathroom and ladybug tiling in Archimedean-like tiling). By determining the eigenmodes and band gaps, complete and accurate band structures and transmission spectra are obtained. Compared to traditional square lattice PnCs, it has been observed that the bands obtained in pattern structures may have some advantages in terms of width and position. It was also shown that the low-frequency response of two Archimedean-like structures was similar with respect to the traditional square lattice.