Topology optimization of isotropic viscoelastic microstructures based on periodic homogenization

TL;DR

This paper develops a topology optimization method for designing isotropic viscoelastic microstructures that effectively reduce low-frequency noise by enhancing damping and impedance matching, outperforming traditional materials.

Contribution

It introduces a complex-valued periodic homogenization-based topology optimization framework for isotropic viscoelastic microstructures with improved noise mitigation capabilities.

Findings

Optimized microstructures outperform constituent materials and simple laminates.

Designs exhibit stable performance across wide frequency bands.

Microstructural engineering effectively mitigates low-frequency noise.

Abstract

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 and independent of orientation. This demonstrates the potential of microstructural engineering for effective low-frequency noise mitigation.