This study proposes a novel phononic-crystal acoustic wave device (AWD). A graphene atomic structure was adopted as the main research subject, and a graphene-like structure was designed using piezoelectric material ZnO and its periodic boundary conditions were defined using the finite element method (FEM). The study conducts acoustic-wave propagation analysis in the frequency domain on the 2D graphene-like structure according to Bloch theory to understand the band gap effects generated by its natural vibration. The effects of shape transformation from a hexagonal honeycomb structure into a regular polygon were also investigated regarding the band gap phenomenon. Thus, this study compared and analyzed numerous 2D polygonal graphene-like structures with a fixed bond diameter (d = 2R =0.7 mm), bonding stick width (0.2 mm), and side length (1 mm), and observed the trends of the band gap changes under natural vibration for designing an optimal AWD; the studied 2D polygonal models were a square, and a regular hexagon, octagon, and decagon.