本文利用擴張晶格聲子晶體，在縱波/聲波下基於量子自旋霍爾效應之理論，利用有限元素法軟體計算週期結構，求得其能帶結構，接下來藉由改變晶格中散射柱的大小來實現拓樸不等價之聲子晶體，之後將兩拓樸不等價聲子晶體組合製造出界面，以超晶胞法分析其能帶結構並且找出邊緣模態，再利用邊緣摸態設計不同界面及傳輸的路徑，驗證所設計的結構具有良好的穿透率且可抑制後向散射等波傳特性，並且與一般缺陷型聲子晶體做比較，最後再結合共振腔的特性，討論當拓樸波導與共振腔結合時，共振腔對於拓樸波導的波傳行為產生的影響，並且與不同的共振腔做比較，將特定頻率的波從波導中分離出來，有關其結果可應用於聲波濾波器。

In this thesis, we propose zone-folding phononic crystal in order to realize the Quantum spin Hall effect in the sound wave system. We calculated the band structure by finite element method. Next, we can get two topologically distinct structure by changing the geometry the scattering rod. Afterward, we utilize two different topologically distinct phononic to manufacture the interface and analysis the band structure by supercell method. The edge mode can be found and we can utilize it to design different interface or transmission path. Compare with defect mode, the edge mode can be verified not only high transmission but also immune backscattering behavior. Finally, we discuss the influence of the resonant cavity on the wave propagation behaviour topological waveguide combined with resonant cavity, and compare with different resonant cavity to separate the wave of specific frequency
Form the waveguide. The result can be applied to acoustic wave filters

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