Bandgap enhancement of two-dimensional lattice metamaterial via re-entrant hierarchy

This paper proposed a one-dimensional (1D) meta-beam through embedding re-entrant hexagons on a 1D single beam. Then a two-dimensional (2D) square resonator lattice with re-entrant hexagons was designed via replacing the ribs with the 1D meta-beams. Based on Bloch’s theorem and finite element method, the dispersions and bandgap properties of 1D meta-beam and 2D lattice with re-entrant hexagon were analyzed. The numerical results indicated that the bandgap property of both structures was improved via embedding re-entrant hexagons. For the 2D square resonator lattice with re-entrant hexagon, the total bandgap width was 34.3% higher than the 2D lattice without re-entrant hexagon. Then a parametric study was implemented, and the results showed the re-entrant ratio, rib thickness and the number of re-entrant hexagons had strong effects on bandgap distribution, especially the re-entrant hexagons, which enhanced the bandgap property in the low-frequency region significantly. Through calculating the contours of group velocity, the anisotropy of the 2D square resonator lattice with re-entrant hexagons was investigated, and the results indicated that there was pronounced caustic at specific parameter sets which reflects energy focus. To verify the bandgap property in the realistic application, the specimen of 2D square resonator lattice with re-entrant hexagons was prepared through additive manufacturing technology, and a low amplitude harmonic test was performed. The experimental result demonstrated the bandgap property of the 2D square resonator lattice with re-entrant hexagons. This paper may introduce a method to enhance the bandgap property of lattice metamaterial.