Labyrinthine acoustic metamaterials with triangular self-similarity for low-frequency sound insulation at deep subwavelength dimensions

Labyrinthine acoustic metamaterials are good choices for realizing sound insulation, acoustic stealth, and acoustic lenses by virtue of their stable performance and rich modes. We design a labyrinthine acoustic metamaterial with eight resonance units by utilizing triangular self-similarity. First, with the help of eigenstate analysis, it is demonstrated that it has monopolar resonance and multipolar resonance modes. Then, the physical mechanisms that generate transmission valleys and acoustic isolation peaks are analyzed by applying the equivalent medium theory and the vibrational velocity field. Finally, we designed an ultra-sparse distribution (fill rate of 20 %) hypersurface for effective acoustic isolation and noise reduction at 417 Hz (normalized frequency of about λ/12). This study can provide useful assistance in the design of labyrinthine acoustic metamaterials, as well as potential applications in areas where ventilation is required (e.g., acoustic barriers for transportation systems).