Study on the multi-low-frequency band gaps and vibration reduction performance of the tooth-shaped acoustic metamaterial

The paper designed two novel tooth-shaped metamaterials based on the tooth-shaped characteristics, including the first order tooth-shaped metamaterial (FOTM) and the second order tooth-shaped metamaterial (SOTM). The SOTM produces an ultra-low band gaps (102.6 Hz) compare of the value of the FOTM (184.5 Hz). Among the first 24 order dispersion curves, the band gap coverages of the FOTM and SOTM can reach 68.5% and 74.1%. Even band gap coverages below 500 Hz still reach 34.1% and 44.8%. While the FOTM owns the maximum bandwidths (688.4 Hz). Next, the band gap generation mechanism of tooth-shaped metamaterials is analyzed according vibration modes. The rotational vibrations in its central part and tooth-shaped ligament parts dissipate the elastic wave energy and generate the band gap by analyzing the iso-frequency contour, group velocity and phase velocity. Finally, the influence of the core tooth-shaped ligaments width and length on the band structure of the FOTM and SOTM are studied. For the FOTM and SOTM, increasing the core tooth-shaped ligament height results in a decrease of the band gap. The design exhibits excellent band gap properties and meets the requirements for lightweight design, and it provides a novel solution for multi-low-frequency wide band.