A novel Star-4 honeycomb with the inclined ligaments for enhanced tunability of wave propagation behaviors

The dynamic mechanical properties of mechanical metamaterials based on the honeycomb structures are widely concerned, especially the wave propagation behaviors. In this study, a novel type of honeycomb is designed by combing the Star-4 structure with the inclined ligaments. A dynamic analysis model of the Star-4 honeycomb with the inclined ligaments (S4HILs) is established based on the periodic description by the Bloch's theorem and the discretization by the finite element theory of Timoshenko beam. The band gap characteristics calculated by the proposed model are compared with the frequency responses obtained by the commercial software to provide the modeling validation. The boundary vibration modes of S4HILs are compared to reveal the formation and closure mechanism of band gap. Moreover, the effects of different types of geometrical features on the band gap distribution and the macro-Poisson's ratio are systematically investigated. The group velocity is finally discussed according to the global dispersion relation to explore the directivity of wave propagation. The results indicate that the inclined ligament can significantly enhance the tunability of wave propagation behaviors, which is mainly reflected in the broadened regulation range of band structure, Poisson's ratio, and group velocity. This work provides an innovative idea for the regulation of wave propagation behaviors though the connection design between mechanical metamaterial unit cells.