Wave propagation characteristics of controllable gyroscopic chiral metamaterials

Abstract

This paper investigates the dispersion characteristics and wave propagation of triangular and concave hexagonal gyroscopic metamaterials. The theory derivations of the dispersion relations are presented and validated through numerical simulations. Group velocity, phase velocity, and wave transmission with different gyroscope torques are analyzed, revealing how the gyroscope torque influences the wave propagation characteristics in the triangular structures. The results indicate that the gyroscope torque breaks the time inverse symmetry, inducing chirality in the triangular structure, and wave predominantly propagates along the spring direction on both low and high frequency dispersion surfaces. On this basis, the concave hexagonal gyroscopic metamaterial is proposed by introducing a transverse long spring, which exhibits two geometric special nodes. Four distinct dispersion surfaces with unique propagation characteristics are generated in the analysis of wave propagation. It is found that the propagation intensity on the first and second dispersion surfaces is highly sensitive to the direction of the gyroscope torque, while wave propagation characteristics of the third and fourth dispersion surfaces exhibit an opposite relationship, in which the Dirac cone is discovered. These findings emphasize that varying the gyroscope torque can achieve the same wave propagation characteristics with different frequencies or change wave propagation with the same frequencies, offering valuable insights for designing metamaterial structures with precise torque distribution control.