Topology design of multi-material soundproof structures including poroelastic media to minimize sound pressure levels

In optimization problems that aim to minimize sound pressure levels, for simplicity, rather than calculating sound pressure directly, elastic structures have been designed so that fundamental eigen-frequencies rigorously depart from excitation frequencies, or so that radiation efficiency is reduced within target frequency ranges. In this paper, we propose a new topology optimization method for the design of soundproof structures consisting of a poroelastic material and an elastic material, which directly minimizes sound pressure levels inside an acoustic cavity by applying damping material to the system. Biot's theory is incorporated into the optimization method to deal with the poroelastic material. The elastic material and the air medium surrounding a soundproof structure are equivalently represented in expressions in agreement with Biot's theory. In this method, a new material interpolation scheme for poroelastic materials based on the density approach is also proposed. Several two-dimensional design problems are presented to demonstrate that the proposed method can provide clear configurations for soundproof structures that reduce sound pressure levels within specified frequency ranges.