Topology optimization of periodic microstructures for enhanced loss factor using acoustic-structure interaction

In this work we present a topology optimization method for the design of 2D composite materials with a distribution of a solid constituent and a lossy acoustic medium for obtaining high loss factors. The method is based on a mixed displacement-pressure finite element (FE) formulation combined with the Bloch-wave condition. We solve the resulting FE eigenvalue problem on a repetitive unit cell with periodic boundary conditions and use a complex k(ω) eigenvalue formulation to compute the loss factor. We consider the optimization problem of maximizing the loss factor in a target frequency range with an additional constraint on the stiffness. In the provided example we demonstrate the effect of combined local resonators and acoustic resonances of similar frequency for creating an enhanced overall loss factor of the material.