Band gap mechanism and vibration attenuation characteristics of the quasi-one-dimensional tetra-chiral metamaterial

In this paper, the quasi-one-dimensional tetra-chiral metamaterial is proposed for low-frequency broadband vibration attenuation, inspired by the 3D chiral compression-torsion coupling metamaterials. Different from the traditional metamaterials utilizing translational local resonators to induce reaction force to prevent vibration transmission, this paper can realize rotation and translation on a resonator by introducing chiral structure, which is more beneficial for vibration energy dissipation. The band gap mechanism and vibration attenuation characteristics of the proposed metamaterial are studied based on the discrete mass-spring model. The dependences of the band gap characteristics on the parameters are studied in detail as the bigger the chiral angle, the bigger the mass ratio, the smaller the stiffness ratio, the smaller the dimensionless rotational inertia, the wider the band gap. The analytical boundary equations for band gaps are derived to provide guidance for desired band gap design, and multiple and ultra-wide band gaps can be obtained by tuning the structural parameters. Through the investigation of eigenstate modes, the mode reversals at dispersion curves intersection and veering are observed, and the interchange mechanism for the boundary equations of dispersion curves is unveiled. The vibration transmission in finite unit cells validates the frequency ranges with high vibration attenuation predicted by band structure. The movement energy analysis and wave packet propagation in finite unit cells also demonstrate the vibration attenuation characteristics of the proposed metamaterial. This study can provide new ideas and theoretical guidance for metamaterial design.

Automated summary

In this paper, a quasi-one-dimensional tetra-chiral metamaterial is proposed for low-frequency broadband vibration attenuation, inspired by 3D chiral compression-torsion coupling metamaterials. The introduction of chiral structure allows rotation and translation on a resonator for better vibration energy dissipation. The band gap characteristics and vibration attenuation properties are studied based on a discrete mass-spring model, with a focus on the dependencies on various parameters and the derivation of analytical boundary equations for band gaps. Multiple and ultra-wide band gaps can be achieved by adjusting the structural parameters. Through eigenstate modes investigation, mode reversals and veering at dispersion curves intersection are observed, revealing the interchange mechanism for dispersion curves boundary equations. Vibration transmission in finite unit cells validates the predicted high vibration attenuation frequency ranges, while movement energy analysis and wave packet propagation demonstrate the vibration attenuation characteristics of the proposed metamaterial. This study provides new ideas and theoretical guidance for metamaterial design.