“…Phononic crystals and metamaterials have attractive potential in elastic wave manipulation and attenuation [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ]. They show promising advantages in the applications of negative refraction [ 2 , 3 ], acoustic cloaking [ 4 , 5 ], wave focusing [ 6 , 7 , 8 , 9 , 10 ], wave attenuation [ 11 , 12 , 13 , 14 , 15 , 16 , 17 ], and vibration-mode tailoring [ 18 ]. The features of phononic crystals and metamaterials stem from Bragg scattering and local resonance, respectively [ 19 , 20 , 21 , 22 , 23 ].…”