Robust elastic wave transport in zone-folding induced topological hierarchical metamaterials

Abstract

The topologically protected elastic wave transport in hierarchical metamaterials for the in-plane mode and out-of-plane mode is investigated in this work. First of all, the influence of two key parameters (the hierarchical order and length ratio) on dispersion relation is studied in detail. It can be found that the introduction of structural hierarchy is beneficial for the formation of low-frequency Dirac cones (DCs). But the number of DCs is independent of the hierarchical order. Moreover, the frequency of DCs and band gaps can be tuned effectively by the length ratio. Tuning the lower-order length ratio is more effective to form low-frequency DCs. Based on above findings, we proposed novel topological hierarchical metamaterials analogue to quantum spin Hall effects (QSHEs) by zone-folding method. By shrinking or expanding the supercell, two types of supercells with distinct topological property are built. In addition, through the dispersion analysis and full-field numerical simulation, topological interface states for both wave modes are obtained successfully, and the robustness is verified also. To overcome the limited frequency range of topological interface states, we try to introduce the temperature-sensitive epoxy into the topological hierarchical metamaterial. Fortunately, the frequency of topological interface states can be tuned in a wide range, and the energy concentration cannot be affected by the temperature. This work will broaden the applied range of hierarchical metamaterials, and is expected to meet the tremendous needs for multifunctional materials in engineering practice.