Design of acoustic metamaterials using an eigenmode-tracking topology optimization approach

Most extraordinary properties of acoustic metamaterials originate from their band gaps, prompting extensive research into designing novel unit cells that achieve broader band gap performance. However, existing optimization frameworks only target direct band gaps while overlooking the underlying vibrational eigenmodes, which may yield narrow band gaps and even exhibit oscillatory behavior with poor convergence. To address this challenge, this study introduces a novel eigenmode-tracking topology optimization framework to maximize the band gaps of acoustic metamaterials. The proposed method continuously tracks eigenmodes during wave-vector scanning across the Brillouin zone and systematically classifies them within the dispersion diagram. This classification enables the optimization to remain targeted at the eigenmodes defining the band-gap boundaries throughout the entire optimization process, thereby preventing eigenmode switching and allowing band gaps to be designed and optimized from the vibration eigenmodes of acoustic metamaterials. Consequently, the framework produces significantly more stable optimization and substantially wider band gaps across multiple eigenmode orders. The physical mechanisms associated with different eigenmodes are also analyzed. To validate the feasibility and effectiveness of the proposed approach, numerical investigations are conducted on a two-dimensional periodic lattice. The results demonstrate that the method markedly enlarges achievable band gap widths across various eigenmode orders.