Ultra-wide band gap in a two-dimensional phononic crystal with hexagonal lattices

Abstract

A new two-dimensional (2D) phononic crystal (PC) constituted by the periodic hexagonal lattices, which is inspired by the scissor-like geodesic circle of the Hoberman sphere, is proposed in this study. The band structures, transmission spectrum as well as displacement field of the proposed PC are analyzed by employing the finite element method (FEM) with the Bloch theorem. Furthermore, the formation mechanism of the band gaps (BGs) is investigated according to the eigenmodes at the BG edges analysis. Results show that the first BG of the proposed PC can be achieved in the range of 244.6 Hz–1490.0 Hz with a gap-mid gap ratio (BG%) of 143.6 %, and it is produced via the rigid body resonance. Also, a BG span from 244.6 Hz to 2543.9 Hz with a BG% of 164.9 % is obtained when an approximate flat band between the first and second BGs is neglected, showing an ultra-wide BG in the low-mid frequency range. We further show that the position and width of the BGs can be adjusted within a broad frequency range by altering the key geometric parameters.