Acoustic band gaps in two-dimensional square arrays of semi-hollow circular cylinders

Concave surfaces focus sound while convex surfaces disperse sound. It is therefore interesting to know if it is possible to make use of these two opposite characteristics to enhance the band gap performance of periodic arrays of solid cylinders in air. In this paper, the band gap characteristics of a 2-D square array of semi-hollow circular cylinders embedded in air are investigated, both experimentally and theoretically. In comparison with the types of inclusion studied by previous researchers, a semi-hollow circular cylinder is unique in the sense that it has concave inner surfaces and convex outer surfaces. The finite difference time domain (FDTD) method is employed to study the propagation behavior of sound across the new phononic crystal of finite extent, and the influences of sample size and inclusion orientation on band gap characteristics are quantified in order to obtain the maximum band gap. For reference, the band gap behaviors of solid circular cylinder/air and hollow circular cylinder/air systems are considered and compared with those of semi-hollow circular cylinder/air systems. In addition to semi-hollow circular cylinders, other inclusion topologies such as semi-hollow triangular and square cylinders are also investigated. To validate the theoretical predictions, experimental measurements on square arrays of hollow Al cylinders in air and semi-hollow Al cylinders in air are carried out. The results demonstrate that the semi-hollow circular cylinder/air system has the best overall band gap performance.