Broadband optimization of volumetric sound metadiffusers

Abstract

Broadband volumetric sound metadiffusers are designed by using gradient-based optimization and by means of multiple scattering theory (MST) employed to evaluate the scattered pressure field by a uniform planar configuration of cylindrical scatterers. The method is illustrated by giving numerical examples for planar configurations of rigid cylinders and thin elastic cylindrical shells situated in the air medium. By rearranging the position of each cylinder, a metadiffuser is optimized to have a high diffusion coefficient. Multiple scenarios are evaluated considering a single frequency and broadband optimization. Single frequency optimization is performed to optimize a configuration of cylinders at a specific wavenumber. Broadband optimization is used to optimize a cylinder configuration for a range of wavenumbers by optimizing the root mean square of diffusion coefficient evaluated at discreet values of normalized wavenumber. MATLAB MultiStart solver combined with parallel computing along with global optimization toolboxes is used to enhance the modeling for optimizing for both scenarios due to its ability to evaluate multiple starting points in parallel, hence being able to find the global optimum. A wide array of metadiffusers is optimized using MATLAB MultiStart and fmincon solvers with the sequential quadratic programming and genetic algorithm for a comparison of performance of these algorithms.