Two-dimensional poroelastic acoustical foam shape design for absorption coefficient maximization by topology optimization method

Optimal shape design of a two-dimensional poroelastic acoustical foam is formulated as a topology optimization problem. For a poroelastic acoustical system consisting of an air region and a poroelastic foam region, two different physical regions are continuously changed in an iterative design process. To automatically account for the moving interfaces between two regions, we propose a new unified model to analyze the whole poroelastic acoustical foam system with one set of governing equations; Biot's equations are modified with a material property interpolation from a topology optimization method. With the unified analysis model, we carry out two-dimensional optimal shape design of a poroelastic acoustical foam by a gradient-based topology optimization setting. The specific objective is the maximization of the absorption coefficient in low and middle ranges of frequencies with different amounts of a poroelastic material. The performances of the obtained shapes are compared with those of well-known wedge shapes, and the improvement of absorption is physically interpreted.