摘要

　　本論文中，以有限元素搭配轉換矩陣法模擬彈性波在一維聲子晶體的波傳行為，討論溫度、晶體結構、缺陷與能隙之間的關係。一維聲子晶體由兩種材料週期排列而成，此結構可阻隔某些頻率的彈性波，此外並利用材料特性對溫度的變化差異，探討溫度與聲子能隙的關係，可作為由溫度調變之濾波器。

　　在週期結構中，適當地破壞聲子晶體之週期性，製造出缺陷，則能在聲子晶體能隙之中產生缺陷模態( defect mode)，在聲子能隙中出現可通過的聲波頻率。將向列型液晶彈性體(nematic elastomers)當成缺陷引入一維聲子晶體結構，討論缺陷厚度對缺陷模態的影響。為了達到主動控制之目的，由於彈性體的硬度比鐵、鋁和形狀記憶合金相較低很多，故在此施以外力改變其缺陷厚度，使其缺陷模態產生變化。另外亦施加電場改變彈性體導軸方向，藉此調變共振模態。藉由上述兩種特性可設計出可調變之共振器。

Abstract

　In this thesis, we apply the finite elment method (FEM) and transfer matrix method (TMM) in simulating the band structure of the one-dimensional phononic crystals. The relation between acoustic band-gap and the phononic crystals structure, such as thickness ratio and the multiple of the thickness are addressed. The temperature sensitivity of the shape memory alloys (SMA) is analyzed. Therefore, the location and width of the band-gap could be modulated by the changes of the temperature and the material propertied. The above mentioned results enables us to design a acoustic filter modulated by temperature.
　By introducing nematic elastomer defect layers into a periodic structure, we create a defect mode that would let the acoustic wave with specific frequency pass through the periodic structure. Because the elastomers are soft in comparison to metals, such as iron, aluminum and shape memory alloys, the thickness of the elastomers defect layers can be extended by applied external forces simply. The quantity and the location of the defect modes are changed with the additional forces. By making use of the tunable defect mode, we can design a acoustic resonator.

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