本論文使用平面波展開法與多重散射法，研究二維聲子晶體中彈性波的行為。由平面波展開法可得出二維聲子晶體中混合波與剪波的頻帶結構，以及無黏滯性流體組成之二維聲子晶體的純縱波頻帶結構，或者是由固體組成的二維聲子晶體之純剪波頻帶結構。我們根據對光子晶體中介電質柱波導之研究，提出與其相似的彈性柱波導結構。藉著引入超晶格，其頻帶結構可被計算，並可找出可傳播模態。我們也對彈性柱波導做彎曲角度變化以及無序排列，以研究其對於穿透率的影響。相信在將來，對於彈性波的應用上，此形式之波導能成為一有用的元件。

In this thesis, we use plane wave expansion method (PWEM) and multiple scattering method to study the propagation behavior of elastic waves in the two-dimensional phononic crystals. The band structure of mixed (longitudinal-transverse) polarization mode and transverse polarization mode can be calculated using PWEM. The band structure for longitudinal polarization mode of two-dimensional phononic crystal composed of non-viscous fluid, and the band structure of transverse polarization mode of two-dimensional phononic crystal of solid can also be calculated. Inspired by the research of dielectric rods waveguide for guiding light, we propose elastic rods waveguide for guiding sound. The band structure of elastic rods waveguide is calculated using super-cell method, and the propagating mode can be obtained. We also consider the effect of bends and disorder on the transmission of the elastic rods waveguide. We believe that this kind of acoustic waveguide can useful in the future.

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