The localization calculation of the layered Period-Doubling, Thue-Morse and sandwich phononic crystals

The calculation of the Lyapunov exponents based on the transfer matrix method is developed to determine the localization factor. The numerical results of the localization factors are given for the layered Period-Doubling, Thue-Morse and sandwich phononic crystals. An analysis depending on the material combinations, layer thickness ratios, layer disorders and incident angles is presented.