Study on the mechanism of band gap and directional wave propagation of the auxetic chiral lattices

In this study, the wave propagation properties in terms of the band gap and directions of wave propagation of the auxetic chiral structure are analyzed. The mechanism of generation of the band gap are carefully investigated. The auxetic chiral structure are assembled with the repeat unit cells and the unit cell contains a number of rigidly connected beams. The dynamic model of the unit cell are established by the principle of finite element method. The wave behaviors of the lattices are calculated by solving the dynamic model with the help of the Bloch's theorem. The band structure are obtained and the effects of the chiral angles on the width and position of the band gap distributions are carefully studied. Especially, the mechanism of formation of the band gap are also analyzed by investigating the vibrational mode calculated by the commercial finite element software. The group velocities are calculated to analyze the effects of the geometrical parameters on the directional frequency-dependent energy flows in the structures. We also use the commercial finite element software to simulate the directional wave behaviors in the structure. We find that the first mode of the elastic wave spread only along certain specific directions in the auxetic chiral structure. The speed of wave propagation will be reduced, and the direction of wave propagation rotates counterclockwise when the chiral angle increases.