Theoretical study on dispersion relations of chiral acoustic metamaterials considering mass-rotation

Low-frequency vibration affects the performance of equipment such as aircraft, ships, automobiles, etc., and the noise caused by vibration harms human health. Acoustic metamaterials can dampen elastic waves at specific frequencies due to their bandgaps. In this work, an acoustic metamaterial structure is designed with the introduction of chirality to obtain wider bandgaps. Considering the rotation of the structural parts, the periodic structure is equivalent to an ideal 6-DOF-model through the introduction of Bloch's theorem, analyzed its dispersion relationship and the influence of structural parameters theoretically, and the vibration characteristics of the structure are given with the help of FEM results. The results show that the designed structure has a local resonance bandgap of around 0.12 and the maximum transmission loss exceeds 40 dB. Parametric analysis of this structure shows that structures with different parameters have up to four bandgaps in total between the second and sixth dispersion curves, and the distribution of the bandgaps is centrosymmetric. Under some parameters, the total bandwidth reaches 83.5% of the total frequency range and reduced the normalized frequency of the first bandgap to lower than 0.07. Compared with existing structures, the newly designed structure has lower bandgap frequency and higher bandwidth, and its theoretical model has outfitted with high efficiency and accuracy. This research can provide theoretical guidance and reference for designing such kinds of acoustic metamaterials.