Designing 2D Phononic Crystal Slabs with Transmission Gaps for Solid Angle as well as Frequency Variation

Abstract

Phononic crystals (PCs) can be used as acoustic frequency selective insulators and filters. In a two‐dimensional (2D) PC, cylindrical scatterers with a common axis direction are located periodically in a host medium. In the present paper, the layer multiple‐scattering (LMS) computational method for wave propagation through 2D PC slabs is formulated and implemented for general 3D incident‐wave directions and polarizations. Extensions are made to slabs with cylindrical scatterers of different types within each layer. As an application, the problem is considered to design such a slab with small sound transmittance within a given frequency band and solid angle region for the direction of the incident plane wave. The design problem, with variable parameters characterizing the scatterer geometry and material, is solved by differential evolution, a global optimization algorithm for efficiently navigating parameter landscapes. The efficacy of the procedure is illustrated by comparison to a direct Monte Carlo method.