Numerical design and optimization of metamaterials for underwater sound absorption at various hydrostatic pressures

Underwater sound absorption materials with a stable performance at various hydrostatic pressures are important for marine applications. However, most studies about underwater sound absorption materials only focused on the performance at atmospheric hydrostatic pressure, while ignoring the influence of various hydrostatic pressures. Aiming to improve the underwater sound absorption stability of a metamaterial at various hydrostatic pressures, different structures and a Nelder–Mead algorithm with an acoustic-structure fully coupled finite element method (FEM) model are developed to optimize the structure of the metamaterial at various hydrostatic pressures. In this numerical modeling, the metamaterial is a PDMS matrix embedded with periodic cylinders. Firstly, the effect of hydrostatic pressure on the metamaterial is evaluated in the frequency range [0, 8 kHz]. Secondly, different cases are designed to improve the underwater sound absorption stability at various hydrostatic pressures, including different cylinder radii, different distances between the air cylinder and the steel backing, and different void shapes. Then two layers of air and/or steel cylinders are introduced to further improve sound absorption performance under various hydrostatic pressures. The results indicate that PDMS with two layers of air cylinders have the optimal sound absorption stability performance under various hydrostatic pressures, which can be attributed to the top layer of air cylinders absorbing the main deformation. Lastly, the optimization algorithm significantly improves the sound absorption performance of the metamaterials at various hydrostatic pressures. This combination of an optimistic algorithm and FEM can guide the design of underwater sound absorption metamaterials at various hydrostatic pressures.