Hybrid TPMS-based Designs for Anisotropic Acoustic Metamaterials: Numerical Simulation and Topology Optimization

Abstract: Anisotropic acoustic metamaterials have received significant scholarly attention in recent years due to their capacity to manipulate wave propagation across various directions. This property is integral to applications involving directional wave guiding. Nonetheless, previously proposed anisotropic acoustic metamaterials exhibited commonalities in bandgaps along x and y periodicities, limiting their efficacy for such applications. Therefore, this work introduces hybrid Triply Periodic Minimal Surfaces (TPMSs)-based anisotropic acoustic metamaterials that manifest abundant bandgap and passband characteristics along the x and y periodicities. Four design families were considered: Primitive-Primitive sheet-based, Gyroid-Gyroid sheet-based, Diamond-Diamond sheet-based, and Nevious-Nevious sheet-based. A computationally efficient exhaustive search was employed to identify optimal hybrid metamaterial designs for various desired audible frequency ranges (i.e., ranging from 20 Hz to 20 kHz). In total, 392,178 designs were assessed in this search. The optimal designs demonstrated pronounced bandgap and passband characteristics across both periodicities, thereby positioning them as promising candidates for directional wave guiding applications. For instance, the optimal Nevious-Nevious sheet-based unit cell design achieved a minimum coverage of 62.90% for bandgaps and passbands within the frequency range of 20 Hz to 5 kHz. Following the identification of optimal unit cell designs, the acoustic pressure responses of hybrid anisotropic acoustic metamaterials, constructed from repeated optimal unit cells, were computed. This involved considering two actuation scenarios, which pertain to exciting the system along both x and y periodicities, revealing responses in alignment with optimized band characteristics.