Ultra-Wide Band Gap in Two-Dimensional Phononic Crystal with Combined Convex and Concave Holes

A phononic crystal with an ultra-wide band gap is proposed, whose unit cell consists of a cross-like concave hole in the center and four square convex holes at the corners. The dispersion relations, modal kinetic energy ratio, and eigenmodes at edges of the band gaps are investigated by using the finite element method. The influence of the geometrical parameters of the convex and concave holes on the band gaps is further analyzed. After optimization, an ultra-wide band gap with gap-to-midgap ratio of 156.0% is achieved, with the filling fraction keeping a relative small value. Numerical results illustrate that the combination of convex and concave holes is a practicable direction for structural optimization of phononic crystals exhibiting ultra-wide band gaps.