Topological interface state formation in an hourglass lattice sandwich meta-structure

Topological interface state formation in elastic structures has attracted extensive research interest. However, most previous studies only explored the topological properties of simple structures, such as plain beams and rods. This study explores the feasibility and methodology of producing topological interface states in hourglass lattice sandwich meta-structures. By extending the spectral element method (SEM), a theoretical framework is developed for analyzing such meta-structures. The results obtained by the analytical model agree well with the finite element (FE) simulation results. Based on the analytical model, we maintain the substrate plates and vary the radii of the struts that constitute the hourglass lattice to explore the topological change. The band inversion is identified in the first band gap by inspecting the band edge evolution pattern. The analysis also indicates that the second band gap does not support topological interface states. Subsequently, the vibration modes at band gap edges are examined to confirm the polarization transition. Based on these analyses, a topological sandwich meta-structure is designed. An ordinary meta-structure without using the topological design strategy is also constructed. Compared with the ordinary meta-structure, a solitary peak occurs on the transmittance curve of the topological meta-structure in the first band gap. The vibration mode at the solitary peak demonstrates that the transverse motion concentrates at the junction interface, exhibiting the typical energy localization behavior of topological interface states.