“…2 Resulting from the destructive interference between incident elastic/acoustic waves and reflections from the scatterers, bandgaps inherently become the basis of the most applications of PnCs. Promising applications of PnCs include sound insulation, 3 sound barrier, 4 damping, 5,6 acoustic resonators, 7,8 elastic/acoustic waveguides, 9 filters, 10 frequency sensing, 11,12 acoustic mirrors, 13 switches, 14 lenses, 15 energy harvesting, 16 negative refraction, 17,18 self-collimation, 19,20 acoustic mirages, 14 rectification, 21 acoustic diodes, 22,23 and thermal conductance. 24,25 In recent years, some researchers have been conducted and focused on topology optimization of photonic crystals (PtCs), 26,27 PnCs [28][29][30][31][32][33] and phoxonic crystals (PxCs).…”