Essential role of material parameters on the band gaps of phononic crystals

In this paper, starting with wave equation, we prove that material parameters determining directly phononic band gaps of the z-mode are the mass density ratio and the shear modulus ratio. Plane wave expansion method is used for calculating band gaps. The influences of these parameters on phononic band gaps are analyzed for different lattices: square and hexagonal. The results show that the maximum band gap appears at both large mass density ratio and shear modulus ratio, and becomes wider with these two parameters increasing. Compared with the shear modulus ratio, the mass density ratio is more important to the appearance of the band gap, but not to the width of the band gap. Only acoustic impedance ratio or wave velocity ratio cannot control band gaps. The results could be helpful in tuning band gaps.