Topology optimization design for total sound absorption in porous media

Abstract

Acoustic porous layers used for noise reduction have the unique functionality of dissipating sound energy. It is very difficult for finite length porous layers to realize total sound absorption if they are filled only with homogeneous materials. Rigid inclusions inserted in a porous medium will certainly alter the acoustic field, realizing total sound absorption at some frequencies, but finding their optimal distributions by trial and error is intractable, especially for multiple target frequencies. The aim of this study is to develop a finite element-based numerical method to distribute rigid inclusions inside a porous layer having a fixed thickness for the total sound absorption. Without any special treatment for initial layout, multiply divided rigid inclusions are distributed systematically in an optimized porous layer by the present density-based topology optimization formulation. Considering single target frequency problems, we initially assess the effectiveness of the developed formulation with regard to achieving total sound absorption. In these problems, various resonance mechanisms, such as the Helmholtz resonance and the quarter-wavelength resonances, are generated inside the porous layer by the distributed rigid inclusions. Subsequently, we solve problems considering multiple target frequencies. The numerical results show that different types of resonances occur appropriately in the optimized porous–rigid layer to achieve total sound absorption simultaneously for all the different target frequencies considered here.