Topology optimization of isotropic viscoelastic microstructures based on periodic homogenization

TL;DR

This work presents a systematic framework to mitigate low-frequency noise by designing isotropic viscoelastic microstructures that simultaneously minimize acoustic reflections and maximize internal damping. It combines complex-valued periodic homogenization with a density-based SIMP topology optimization within a symmetric unit cell (honeycomb) to derive effective complex properties and guide material distribution. The resulting optimized microstructure, largely comprising impedance-matching material with a connected viscoelastic network, achieves superior attenuation while maintaining low reflectivity and orientation-independent performance, outpacing its constituent materials and simple laminates. The approach offers a practical design pathway for broadband low-frequency noise control in structural applications, validated by both homogenization-based predictions and full-wave simulations.

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.

Figures (5)

• Figure 1: Model of a low-reflection and high-damping structure. (a) Illustration of the design problem. (b) Schematic of the viscoelastic composites. (c) The unit cell comprises two phases: impedance-matching material and viscoelastic material. The periodic structure is homogenized in the limiting case $a \to 0$.
• Figure 2: Half-plane filled with a viscoelastic material.
• Figure 3: Flowchart of the optimization method.
• Figure 4: Histories of the optimized design process. (a) History of the volume fraction of the viscoelastic material and unit cell designs at steps 0, 20, 50, and 100. (b) History of the objective functional $J'_1:= \sqrt{J_1}$ and $J_2$. The square root of $J_1$ is used to better visualize its convergence.
• Figure 5: Schematic of the verification method and results. (a) $x_2$-periodic computational model and boundary conditions for verification. $N$ layers of unit cells are used to compare the performance of the optimized design and the $\phi$-tilted laminate structure. (b) Numerical results of the absorption coefficient $1-R/I-T/I$ and transmission coefficient $T/I$.