Analysis of the existence of complete band gaps in periodic binary piezoelectric phononic crystals based on connectivity

In this paper we analyze the existence of complete band gaps in periodic binary two-dimensional piezoelectric phononic crystals with {1-3} connectivity family from a point view of connectivity. For this structure and no wave-vector components parallel to the cylinders, there are two independent modes of vibration. One of them is the transverse polarization mode (Z mode) with the elastic displacement vector parallel to the cylinders. And the other one is the longitudinal-transverse polarization mode (XY mode) with the elastic displacement vector perpendicular to the cylinders. The plane-wave-expansion (PWE) method is applied to the theoretical derivation of secular equations of the two polarization modes. Band structures for the two modes are calculated to look for complete band gaps in piezoelectric phononic crystals with both 1-3 connectivity and 3-1 connectivity, which will be used to analyze the effect of connectivity on the existence of band gaps in piezoelectric phonic crystals. Numerical results reveal that the strong difference of physical properties between the constituents in piezoelectric phononic crystals can´t dominate the existence of complete band gaps and the connectivity of the constituents plays an important role in the existence mechanism.