Tunable wave propagation in octa-chiral lattices with local resonators

摘要

This paper aims to investigate the wave behavior of the octa-chiral lattices with local resonators and tunable wave propagation properties with different chiral geometrical dimensions. The octa-chiral lattices are assembled with the repeat unit cells and the unit cell contains a ring and eight slender elastic massless ligaments which are rigidly connected to the ring. The ring has a heavy disk with its surrounding soft elastic annulus. The dynamic equations of the lattices are established with the principle of the Lagrangian method. The wave behaviors of the lattices are calculated by solving the eigenvalue problem governing the wave harmonic propagation with the application of the Bloch's theorem. By calculating the band structures and the phase and group, we investigate the effects of the chiral geometry and resonators on the formation of the low-frequency band-gaps and the directional frequency-dependent energy flow. The phase and group velocities show that the maxima wave propagation speeds are along the +/- 45 degrees. While, the phase velocities and the group velocities trend to be identical with the increase of the chiral angles. The findings suggest that we can tune the anisotropic wave behavior to the isotropic wave characterization with special structural design on the chiral geometry.