Projection band structure of V- and T-type PCs. Panels (a) and (b) are projection band structures of a spliced structure of a V-shaped phononic crystal with θ = 20° and −20° (10 layers each) in the x and y directions, respectively. The gray area indicates the bulk state, and red dotted line indicates the edge state. Panels (c) and (d) are projection band structures of a spliced structure of a T-type phononic crystal with θ = 60° and −60° (10 layers each) in the x and y directions, respectively. The illustrations in (a)–(d) show the distributions of sound pressure around the splicing boundary at different wave vectors. The black arrows represent the energy flow directions.