Phononic Localization in Locally Resonant Ternary Thue-Morse and Rudin-Shapiro Structures

Abstract

The wave localization properties in locally resonant ternary phononic aperiodic crystals based on Thue-Morse and Rudin-Shapiro sequences, are theoretically investigated by the transfer matrix method. The various factors affecting localization characteristics are discussed. Numerical results show that the effect of material properties and the geometric structure parameters on the number and size of band gaps is obvious. Moreover, compared with the corresponding binary aperiodic structures without local resonances, the localization factors become larger in the locally resonant ternary structures. And wider and lower-frequency band gaps and localized resonant flat bands appear in the locally resonant aperiodic system. Compared with the locally resonant Thue-Morse system, the localization factor becomes larger and the band splitting phenomenon is less obvious in the locally resonant Rudin-Shapiro system, which is just the opposite to that in the aperiodic system without local resonance. This study is useful in filter, waveguide, and so on.