Acoustic band gaps with diffraction gratings in a two-dimensional phononic crystal with a square lattice in water

Abstract

The present work reports a combined experimental and theoretical study on the acoustic band gaps in a two-dimensional (2D) phononic crystal (PC) consisting of periodic square arrays of stainless-steel cylinders with diameters of 1.0 mm and a lattice constant of 1.5 mm in water. The theoretical band structure of the 2D PC was calculated along the ΓX direction of the first Brillouin zone. The transmission and the reflection coefficients were obtained both experimentally and theoretically along the ΓX direction of the 2D PC. The 2D PC exhibited 5 band gaps at frequencies below 2.0 MHz, with the first Bragg gap being around a frequency of 0.5 MHz. To understand the band gaps in the 2D PC, we calculated the acoustic pressure fields at specific frequencies of interest for normal incidence, and we explained them from the perspective of acoustic diffraction gratings.

Acoustic band gaps due to diffraction modes in two-dimensional phononic crystals

“…When the waves at band gap frequencies are normally incident on the PC, only normal reflection occurs at certain band gaps, and additional reflected waves with different propagation directions occur at other band gaps. 24) According to the diffraction grating equation, the normally reflected wave is caused by the zeroth order diffraction mode, and additional reflected waves are caused by the non-zeroth order diffraction modes. Based on these diffraction modes, we classify the acoustic band gap into two types: type A and type B.…”