Study on band gaps of elastic waves propagating in one-dimensional disordered phononic crystals

Band gaps of elastic waves, both in-plane and anti-plane waves, propagating along arbitrary direction in one-dimensional disordered phononic crystals are studied in this paper. The localization of wave propagation due to random disorder is discussed by introducing the concept of the localization factor. As a special case between ordered and disordered structures, we analyze the properties of the band gaps of phononic crystals with quasi-periodicity (i.e. phononic quasicrystals). Compared with the periodic structure, phononic quasicrystals involve more bands with localization of wave motion. The transmission coefficients are also calculated and the results show the same behaviors as the localization factor does. Therefore, the localization factor may act as an accurate and efficient parameter to characterize band structures of both ordered and disordered (including quasi-periodic) phononic crystals.