Topology optimization framework for defective metastructures with simultaneous frequency and mode matching

초록

Acoustic metastructures with defects can generate localized defect bands within acoustic band gaps, thereby enabling strong acoustic energy localization. However, the performance of these defect-incorporated devices depends not only on the defect-band frequency but also on the associated defect-mode shape, which governs the spatial distribution and concentration of acoustic energy. Previous topology optimization studies have primarily focused on frequency matching or localization enhancement; however, the simultaneous control of defect-band frequencies and defect-mode shapes has received relatively little attention. This study addresses this limitation by presenting a two-stage topology optimization framework for acoustic metastructures with line defects that simultaneously achieves defect-band-frequency and defect-mode-shape matching. The proposed framework consists of two steps. First, unit-cell optimization is performed to maximize the normalized band-gap width. Second, line-defect optimization is conducted to minimize the mismatch between the defect-band frequency and the prescribed target frequency, all while satisfying a constraint based on a weighted modal assurance criterion for matching defect modes. To improve manufacturability, a parameterized design is derived from the optimized topology and refined through size optimization. Numerical results demonstrate that the proposed framework successfully generates a localized defect band at the prescribed target frequency while accurately reproducing the desired defect-mode shape. Additional investigations at different target frequencies reveal distinct optimized topologies associated with different band-gap formation mechanisms. These results highlight the capability of the proposed framework to systematically control both the spectral and modal characteristics of defect states, providing an effective design strategy for acoustic metastructures in high-performance sensing, transduction, and energy-harvesting applications.

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