Transmission Properties Of One-dimensional Quasi-periodical Phononic Crystals

Phononic crystals belong to the field of artificial micro-structural composite materials of acoustic or elastic wave, the most important feature of which is the existence of band gaps. The characteristics of the phononic crystals not only hold abundant physical contents, but also can be used in the fabrication of the filters or guides of acoustic or elastic wave, so more and more attentions have been devoted to the field of phononic crystals. One of the important aspect of which is the localized state in phononic gaps.The models of one-dimensional (1D) phononic crystals with quasi-periodical structures are proposed for the first time, including the structures of two-component generalized Fibonacci, Thue-Morse, three-component generalized Fibonacci and Fibonacci-class. The main idea of this thesis is producing the localized state in the band gaps by using of quasi- periodical structural phononic crystals instead of traditional defect structures. Based on the theory of eigen-mode matching, we have calculated the transmission coefficients of the above structures and investigated the properties of phononic localized states when the elastic waves pass through those 1D quasi-periodical phoninic crystals. These studies are helpful to the application field of phononic crystals.The results show that the band gaps can also be found in the phononic crystals with the quasi-periodical structure, and there are more strongly localized resonant modes in the gaps of the quasi-periodical phononic crystals. The effect of quasi-periodical structure is same as that of which the defects were arranged in the periodical phononic crystals. But different quasi- periodical structures have different localized resonant modes. The structure of B-class generalized Fibonacci phononic crystals are expected to be used in the elastic wave-guides, the others could be used in the elastic wave-filter. However, the thickness of the system and the angle of incident waves also influence the frequency of wave-guide and the quality factor of resonant modes.