聲子晶體是由兩種材料所組成，一個稱為填充體，另一個則稱為母材。藉由調整填充體與母材之間的週期性，與兩者材料之間的匹配性，通過聲子晶體的聲波於某些頻帶會有無法傳遞之現象，此種現象稱之為頻溝。頻溝的現象是由於符合布拉格定理而產生建設性干涉導致聲波強烈的反射，亦是本研究主要探討的機制。
本文藉由邊界元素模擬軟體BEASY分析固-流組合而成之二維聲子晶體聲場特性，並以入射前後之相對振幅呈現聲子晶體發生頻溝之頻帶。首先針對Varadan與Faran兩位學者所研究的單一剛性圓球與圓柱體在水中的散射聲場進行邊界元素模型之模擬，比對在不同波數半徑積的變化下其散射聲場之結果；接著模擬Sánchez-Pérez等人研究由不鏽鋼與鋁作為填充體、空氣作為母材之二維聲子晶體在正方晶格與三角晶格的邊界元素模型，並以單頻掃頻的方式比對文獻中發生頻溝之頻帶，綜合[100]與[110]方向入射之結果，可計算求得全頻溝發生之區間。最後本文針對了聲子晶體的聲場散射圖樣作討論，以試圖了解聲子晶體在聲源的作用下，其聲壓在空間中的分佈情形，因而可以藉由改善聲子晶體的結構來達到降低噪音的影響。
本研究成果已成功建立邊界元素模擬分析固-流組合成之二維聲子晶體模型，經由比對文獻結果已驗證本模擬之可行性與準確性，這將証明邊界元素法可成為未來聲子晶體在設計成為新型吸（隔）音材的一項有利分析工具。

“Phononic crystal,” a binary-composite medium composed of a square array of parallel circular steel cylinders in a air matrix is studied. Phononic crystal exists full band-gaps phenomenon which is caused by strongly constructive interference of Bragg reflection in their acoustic transmission spectrum. The Bragg reflection theorem is also a basis for searching the full band-gaps in this thesis.
This thesis applies the boundary element simulation software BEASY to analyze the sound field characteristics of solid/fluid composite medium, phononic crystal. The forbidden bands of the band gap are shown by the relative amplitude in the incidence before and after. First, the study by Varadan and Faran aims at scattering sound field of the single rigid sphere and the circular cylinder in water which constructed a simulation of the boundary element model. It is compared to under the different kr change result of its scattering sound field and it has demonstrated that our simulation work was feasible. Second, the study constructs the boundary element model for a two-dimensional phononic crystal which was studied by Sánchez-Pérez etc. with experimentation, constituted of rectangular and triangular array of parallel circular stainless steel and aluminum cylinders in air. The study is compared with the forbidden bands of the band gap in the reference which performs the simulations with the mono-frequency by sweep. The full band gaps are determined from the combination of the results in both the [100] and [110] direction. Finally, the study aimed at the scattering pattern of sound field in phononic crystal to make discussion. In order to understand the sound source acts on the phononic crystal, the status of the sound pressure is distributed over the spatial. So it could get up to reduce the influence of the noise by way of the improvement the structure in phononic crystal.
The study has successfully shown the boundary element simulation for the solid/fluid phononic crystal. The study of experiment in the reference is compared with the BEM simulation in this thesis. The results have demonstrated that the boundary element method is a good tool for the design of phononic crystal in application to new type sound absorption (isolation) material in the future.

摘要 I
ABSTRACT III
目錄 V
表目錄 VII
圖目錄 VIII
第一章 緒論 1
1-1前言 1
1-2文獻回顧 4
1-3研究動機與目的 6
第二章 基本理論 8
2-1 聲學相關理論[27] 8
2-1-1 波動方程式 8
2-1-2 聲波的反射、透射與散射 9
2-1-3 剛性圓球的散射聲場 10
2-2 聲子晶體相關理論 10
2-2-1 二維晶格種類 10
2-2-2 晶體晶格與倒晶格（Reciprocal Lattice） 12
2-2-3 填充率（Filling Fraction） 13
2-2-4 布拉格定理（Bragg Law） 14
2-2-5 布里淵區（Brillouin Zone） 16
2-2-6 [100]與[110]方向指數 17
2-3 邊界元素法原理 19
2-3-1 邊界元素法概述 19
2-3-2 以邊界元素法模擬聲場變化 20
2-3-3 邊界元素軟體介紹與處理步驟 22
2-3-4 使用元素介紹 24
第三章 數值模擬方法及步驟 39
3-1 模擬目的 39
3-2 模擬設定及步驟 40
3-3 模擬數據處理 42
第四章 理論與模擬結果 50
4-1 數值模擬與文獻理論的散射圖樣比對 50
4-2 數值模擬與文獻聲子晶體的頻溝結果比較 52
4-3 數值模擬計算全頻溝 57
4-4 討論數值模擬聲子晶體的散射圖樣 59
第五章 結論與未來研究方向 89
5-1結論 89
5-2 未來研究方向 90
參考文獻 92

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