Topology optimization of isotropic viscoelastic microstructures based on periodic homogenization

Mitigating low-frequency noise is particularly challenging due to its limited natural attenuation. This study aims to design viscoelastic composite microstructures that achieve both low acoustic reflection and high internal damping by simultaneously enhancing their effective acoustic impedance and attenuation characteristics. Using complex-valued periodic homogenization theory and density-based topology optimization, viscoelastic and impedance-matching materials are designed within a highly symmetric unit cell to manipulate these isotropic properties. Numerical results show that the optimized isotropic design robustly outperforms its constituent materials and simple anisotropic laminate structures, exhibiting performance that is stable across a wide frequency band, independent of orientation, and stable across various structural scales. This demonstrates the potential of microstructural engineering for effective low-frequency noise mitigation.