Acoustic Band Structures in Two-dimensional Phononic Crystals with a Square Lattice in Water

Phononic crystals are composite materials consisting of a periodic arrangement of scattering inclusions in a host material. One of the most important properties of phononic crystals is the existence of band gaps, i.e., ranges of frequencies at which acoustic waves cannot propagate through the structure. The present study aims to investigate theoretically and experimentally the acoustic band structures in two- dimensional (2D) phononic crystals consisting of periodic square arrays of stainless steel solid cylinders with a diameter of 1 mm and a lattice constant of 1.5 mm in water. The theoretical dispersion relation that depicts the relationship between the frequency and the wave vector was calculated along the GX direction of the first Brillouin zone using the finite element method to predict the band structures in the 2D phononic crystals. The transmission and the reflection coefficients were measured in the 2D phononic crystals with 1, 3, 5, 7, and 9 layers of stainless steel cylinders stacked in the perpendicular direction to propagation at normal incidence. The theoretical dispersion relation exhibited five band gaps at frequencies below 2 MHz, the first gap appearing around a frequency of 0.5 MHz. The location and the width of the band gaps experimentally observed in the transmission and the reflection coefficients appeared to coincide well with those determined from the theoretical dispersion relation.