Study on the bandgap and directional wave propagation mechanism of novel auxiliary semicircle rings lattices

Abstract

In this study, a novel auxiliary semicircle rings lattice is proposed, and the proposed structure consists of connecting ligaments and auxiliary semicircle rings on ligaments. The bandgap and wave propagation characteristics of the proposed structure are analyzed. The generation mechanism of bandgap is carefully studied according to the vibration shape of the structure. Based on the Bloch's theorem and the finite element method, the dynamic model of the structure is solved to explore the wave behavior in the lattice. Then, the effects of different semicircle directions, the number of semicircle rings and the size of semicircle rings on the bandgap width and position are analyzed. In particular, we calculated the group velocity to analyze the influence of the direction of the semicircle rings on the directional frequency related energy flow in the structure. We also simulated the directional wave behavior in a finite-size lattice. It was found that in the proposed structure, the elastic wave with a specific frequency propagated along a certain direction. This study provides an ideological guidance for the topology design of metamaterials with directional wave propagation.