The wave attenuations in phononic crystals based on unit cell and supercell relationship
Abstract
The reduction of the periodicity of phononic crystals (PnCs) usually leads to the decrease of band gap (BG) width. However, a systematic study of the relationship between the unit cell and the supercell in the proposed hybrid stepped PnCs shows that the BG width can be increased in special cases. How the periodicity of PnCs affects the final BG characteristics is important for the design of PnCs with high structural performance. Supercell of PnCs with imperfections from the rotation of the unit cell was used to demonstrate the relationship between the unit cell and the supercell, which was further used for the wave attenuations of the proposed hybrid stepped PnCs. The rotation angle and the number of the rotating scatterers can be controlled for better structural performance for the PnCs. The different changes of the equivalent stiffness corresponding to the starting and the end frequencies lead to the increase of the BG width when the ration angle of the unit cell is 35∘35∘ in the supercell composed of zigzag scatterers and cross scatterers. The rotation of the unit cell in the supercell leads to the decrease of the starting frequency.
