Investigation of sound insulation properties of triply periodic minimal surfaces using band structure analysis

Some butterfly wings exhibit vivid structural colors due to microscopic architectures based on a triply periodic minimal surface (TPMS) known as the Gyroid. This structure reflects specific wavelengths of light by forming photonic band gaps. Inspired by this phenomenon, we explore the application of TPMS in acoustic metamaterials. TPMS offers smooth, continuous geometry and possesses interconnected voids, which not only enable the formation of acoustic band gaps but also suggest potential for airflow and ventilation. The aim of this study is to develop effective sound insulation materials based on TPMS structures. Previous investigations have shown that TPMS can exhibit sound insulation at specific frequencies when subjected to normal incidence, and that compressing the structure along a single axis enhances this performance. However, it remains unclear whether TPMS possesses isotropic phononic band gaps. In this work, we conduct band structure analysis to investigate the isotropy of the acoustic band gaps in TPMS. Additionally, we examine how geometric deformation—such as uniaxial compression—affects the formation and characteristics of these band gaps.