Calculation of band structures of a phononic crystal within a waveguide in 3D with cubic inclusions using a Periodic Green’s Function Method

Abstract

The Phononic Crystals have generated a growing scientific interest as a means to control the dispersion of waves in various technological applications such as telecommunications. In particular, Phononic Crystal Waveguides are composed of periodic distributions of dispersers immersed in a propagation medium and, designed by an arrangement with dimensions and periods comparable to the wavelength. These crystals have properties that give them the ability to guide acoustic waves efficiently. In this paper, we present a numerical Boundary Element Method, which requires the use of a Periodic Green’s Function. This method allows to calculate the band structure of phononic crystals in two- and three-dimensions. In particular, the band structure is calculated for a waveguide formed by two flat, and parallel plates that involve a two-dimensional periodic arrangement of cubic inclusions. All surfaces involved are considered acoustic hard surfaces. The system considered, in addition to being a waveguide is in itself a phononic crystal, so that this type of systems present an alternative to manufacture to phononic crystal that can act as a phononic crystal and as an acoustic waveguide. These properties present some interest from a technological point of view.