Low-Frequency Bandgap Characteristics of a Graphene-Inspired Two-Dimensional Twisted Bilayer Composite Phononic Crystal

Abstract

Abstract. This article presents a two-dimensional composite phononic crystal with a graphene-inspired twisted bilayer configuration. The structure consists of tungsten-rubber core–shell scatterers embedded in an elastic matrix and arranged in a honeycomb lattice. A minimal unit cell was constructed, and finite-element calculations were performed to investigate the low-frequency bandgap characteristics of the structure. By systematically varying the geometric parameter q, the independent dimensions of the core and coating, and the twist angle θ, the effects of geometric scaling and twisting on the first two low-frequency bandgaps were analyzed. The results show that the low-frequency bandgap characteristics exhibit a pronounced nonmonotonic dependence on q, while independent scaling of the core and coating dictates the bandgap frequency position and width, respectively. Under the representative geometric condition of q=2.5, twisting significantly modifies the bandgap structure by broadening the low-frequency bandgap range, particularly the second bandgap, and shifting the first bandgap toward lower frequencies. In addition, the twist angle provides an additional geometric degree-of-freedom for tuning both bandgap width and frequency position. Finite-structure wave propagation simulations and frequency-response analysis further confirm that elastic-wave transmission is effectively suppressed within the predicted bandgap ranges, in good agreement with the band structure calculations. These results show that the proposed twisted bilayer model provides an effective strategy for designing low-frequency phononic crystals and regulating low-frequency elastic-wave propagation.