The mechanism of bandgap opening and merging in 2D spherical phononic crystals

Highlights: • A spherical phononic crystal model with ultra-wide low frequency bandgap is designed. • The bandgap opening and merging behavior of hybrid phononic crystals model is analyzed. • An effective torsional vibration equivalent model and frequency calculating formula are proposed. A self-contained theoretical analysis of the bandgap opening and merging behavior for the designed phononic crystal model which is composed of three-component coated ball and four short connecting plates is reported in this study by finite element numerical simulations. The results show that there are multiple bandgaps of the designed model in the middle and low frequency range simultaneously. The structure symmetry is reduced to open a new bandgap via the separation of resonance modes, and an ultra-wide bandgap obtained. Especially, the equivalent spring mass model is constructed and the corresponding calculation formula of torsional resonance frequency is presented. In addition, the influence of the structural parameters on the band structure is investigated.