聲子晶體是由兩種材料所組成，一個稱為填充物，另一個稱為母材。藉由調整填充物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。頻溝的現象是由於布拉格反射產生的破壞性干涉所造成，亦是本研究主要探討的機制。
由於聲子晶體頻溝的特性，將之應用於水中吸音材料極為合適。本研究擬分析一銅-水組合的二維聲子晶體全向性頻溝，實驗中聲子晶體包含三種填充率分別為5 ％，10 ％及20 ％，並且使用300 kHz，500 kHz及1 MHz等三種中心頻率的探頭(三種探頭的頻寬分別為210 kHz~390 kHz，350 kHz~650 kHz，及700 kHz~1300 kHz)，進行[100]與[110]方向的量測。在本研究所設計聲子晶體的頻溝，是針對實驗室成對最低頻探頭300 kHz而設計，另外再輔以500 kHz與1 MHz探頭進行實驗比對。雖然目前水下音響裝置實際使用的頻率在15~200 kHz，並不在本研究討論的頻率範圍(210 kHz~1300 kHz)，但本研究設計聲子晶體頻溝的方式，卻也間接驗證聲子晶體應用在水中吸音材料是可行的。
另外，在本研究中發現，每5 kHz單頻量測頻溝的結果，和使用超音波分析儀激發全頻寬脈衝波的頻溝量測結果趨勢一致，可以先進行探頭全頻寬量測找出頻溝可能位置，再進一步使用單頻量測細部討論頻溝邊緣陡降部分。利用全頻寬量測搜尋頻溝的方式，有無置入聲子晶體以10 dB聲能降作為判斷實驗頻溝的依據；這代表當聲子晶體置入水中時，以及尚未置入聲子晶體時的情況，兩者能量相差10倍左右，這是因為聲子晶體在水中將聲能降低了10 dB。本實驗的結果顯示全頻溝範圍為340 kHz~420 kHz(填充率20 ％)，310 kHz~370 kHz(填充率10 ％)，230 kHz~240 kHz(填充率5 ％)，280 kHz~285 kHz (填充率5 ％)；並使用布拉格反射理論來粗估頻溝位置，確實能預測n=1~3之全頻溝。這也證實了若在水中放置此種由聲子晶體組成的新型吸音材料，便能達到特定頻率下匿蹤的效果。而本研究採用的布拉格反射理論預估頻溝位置之方式，對於未來設計各種不同組合的聲子晶體吸音材料，亦有正面的幫助。

“Phononic crystal,” a binary-composite medium composed of a square array of parallel circular brass cylinders in a water matrix is reported. Phononic crystal exists total band-gaps phenomenon which is caused by destructive interference of Bragg reflection in their acoustic transmission spectrum. This Bragg reflection theorem is also a basis for searching the total band-gaps in this thesis.
Because of the band-gaps of the phononic crystal, it is very appropriate for applying phononic crystal in underwater absorptive materials. This research presents the Bragg theorem prediction of brass/water acoustic forbidden bands structure with three kinds of different filling fractions, 5 %, 10 %, and 20 %, and three kinds of transducers. Their central frequency are 300 kHz, 500 kHz, and 1 MHz, respectively, and their bandwidths are 210 kHz~390 kHz, 350 kHz~650 kHz, and 700 kHz~1300 kHz, respectively. Furthermore, in order to find total band-gaps, [100] and [110] directions are measured in this research. The band-gaps of phononic crystal in this research are designed by the couple probes of lowest frequencies 300 kHz in our laboratory. Although the devices of underwater acoustics usually operate in 15~200 kHz, it is also proved indirectly that to design and to apply phononic crystal in underwater absorptive materials are workable.
In addition, the measurement results of band-gaps of single frequency are the same as broad-band frequencies using ultrasonic analyzer in this thesis. Therefore, it is a good way to survey the band-gaps with broad-band frequencies method first, and then to use single frequency method measuring deeply drop of the band-gaps.
This research uses Bragg reflection theorem, to calculate approximate position of band-gaps, and predicts n=1~3 total band-gaps successfully in experiments. It is also proved that using this kind of underwater absorptive materials of phononic crystal has the effect of camouflaging submarine purpose with specific frequencies. This is an easiest theorem to survey band-gaps of phononic crystal, and must be a most useful tool to design all kinds of absorptive materials of phononic crystal.

目錄 1
表目錄 4
圖目錄 5
中文摘要 9
英文摘要 11
第一章 緒論 13
1-1 前言 13
1-2 文獻回顧 14
1-3 研究動機與目的 17
1-4 章節說明 18
第二章 基本理論 19
2-1 二維晶格種類 19
2-2 晶體晶格與倒晶格(Reciprocal Lattice) 20
2-3 填充率(Filling Fraction) 22
2-4 布拉格定理(Bragg Law) 22
2-5 布里淵區(Brillouin Zone) 24
2-6 [100]與[110]方向指數 26
2-7 平面波展開法(Plane Wave Expansion, PWE) 27
2-8 頻溝產生的機制 28
第三章 二維聲子晶體製作、實驗設定與架構 37
3-1 實驗目的 37
3-2 二維聲子晶體製作過程 38
3-3 二維聲子晶體實驗設備 39
3-4 聲子晶體試件規格 42
3-5 實驗設定與架構 43
3-5-1 探頭遠場的安置 44
3-5-2 實驗中各個水路的影響 45
3-5-3 單頻的選用 46
3-5-4 含頻寬的選用 46
第四章 實驗量測結果與討論 63
4-1 單頻量測與全頻寬量測實驗結果比較 63
4-2 頻溝之預測 64
4-3 頻溝與層數的關係 70
4-4 實驗可能造成之誤差 71
第五章 成果與討論 86
5-1 本文結論 86
5-2 本文成果 87
5-3 尚待研究的方向 88
5-4 未來應用領域 88
參考文獻 90
附錄A、二維聲子晶體聲場模擬 93
附錄B、聲波於水中之衰減 97

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