Tailoring of interiorly resonant band gaps in structurally square re-entrant honeycombs

The tailoring of interiorly resonant band gaps in structurally square re-entrant honeycombs (SSRHs) characterized by a high connectivity that eight folded sheets jointed at each vertex is investigated. Special attention is devoted to the influence of variations induced through the alteration of mechanical properties of local parts of sheets or lattice geometry on the elastic wave propagation in SSRHs. Band structures of these two types of modified honeycombs are calculated by means of the finite element technology in conjunction with Blochs theorem. Interiorly resonant band gaps, related closely to the flat propagation modes and the rotational modes, are present in both altered configurations. Furthermore, heuristic models, proposed according to the deformation characteristics of the resonant modes, provide a precise estimation to the interiorly resonant band gap involving its position and extent, thus offering a rational analysis to assess the band gap tunability. This predictable robustness of the heuristic models for the interiorly resonant band gaps suggests the potential of SSRH as a host structure in the active control to the propagation of elastic waves.