Topology optimization of anechoic coating for maximizing sound absorption

Anechoic coatings, attached to the surface of underwater vehicles, are an effective way to absorb the incident sound from active sonars. It is well known that a homogeneous viscoelastic material layer with limited thickness does not provide significant sound absorption performance, thus, anechoic coatings embedded with air cavities are being used for underwater applications. Previous optimization works on this type of anechoic coating mainly focused on the geometrical parameters, position and shape of the internal cavity, while ignoring the influence of the material distribution configuration. In this research, we propose a topology optimization formulation that can directly determine the optimal material layout. A method combining the Bloch theory and finite element method (FEM) is adopted to analyze the sound characteristics of a unit cell model, which is able to represent the whole periodic structure. The proposed optimization formulation employs a reflection coefficient to form the objective function under zero transmission backing conditions. Sensitivity analysis is explicitly presented for the utilization of the typical gradient based optimization method. Finally, numerical examples are provided to demonstrate the validity and significant enhancement in the absorptive performance of anechoic coatings achieved by the proposed methodology. The influence of material distribution on macro level and further research emphases on low frequency reduction are also discussed.