Fig. 2

Comparison of the dispersion curves and band gaps of dielectric phononic crystal based on three models. a Classical elasticity \((l=0,{l_1}=0,f=0,L=0,{L_1}=0,F=0)\); b gradient elasticity \((l={10^{ - 5}},{l_1}=2 \times {10^{ - 5}},f=0,L=5,{L_1}=5,F=0)\); c flexoelectric and gradient elasticity \((l={10^{ - 5}},{l_1}=2 \times {10^{ - 5}},f={10^{ - 5}},L=5,{L_1}=5,F=20)\).