本文應用Biot多孔線性彈性動態方程組於拉普拉斯域推導多孔吸音材料之動態複數勁度再計算其吸音係數，並分析空間聲場之特性，文中也針對聲場統御方程式之推導詳加說明。為探討空間聲場之特性，本文將分析方法歸納為二部份，第一部份應用拉普拉斯轉換後之多孔線性彈性動態方程以二維矩形多孔彈性元素及 Galerkin有限元素法推導並進行有限元素頻域分析(FEFDA)。第二部分應用聲場波動方程式配合二維矩形元素進行聲場有限元素分析(AFFEA)。
FEFDA應用空氣層與泡棉材料參數與邊界設定進行一維及二維含有吸音層聲場之響應分析，並與AFFEA結果進行比較。由同網格數之分析結果可發現AFFEA之模態頻率誤差較FDFEA大，且在含有吸音層之聲場分析中，AFFEA需輸入以FEFDA完成之吸音材料聲響阻抗才能進行分析。此外在高頻時AFFEA必須在高網格數下才有較精確之結果。兩種分析亦同時顯示於室內空間聲場設置吸音材料後因受限吸音材料特性，在低頻時效果不佳，但隨著頻率增高後整體吸音效果顯著提升。本文發展之FEFDA也可應用於模擬阻抗實驗，經分析發現模擬之吸音係數也與一維理論解幾近吻合。

In this study, Biot's poroelastic dynamic equations were applied to analyze the dynamic stiffness and the sound absorption coefficient of the sound absorption material and to analyze the indoor acoustics.  For comparison purposes, the acoustic wave equation was also applied to evaluate indoor acoustics.  Two finite element analyses were conducted.  First, the poroelastic dynamic equations were transformed to Laplace domain and the Galerkin finite element approach is applied to derive the stiffness matrix of rectangular porous element for conducting the finite element frequency domain analysis (FEFDA).  Secondly, the acoustic wave equation is used derive the stiffness matrix of acoustic rectangular element for performing the acoustic field finite element analysis (AFFEA).
Using foam material properties and suitable boundary conditions, the FEFDA was applied to evaluate the frequency response functions of one-dimensional and two-dimensional indoor acoustics and the results were compared with that obtained by the AFFEA.  Based on the same element meshes, the results showed that the errors on modal frequencies of AFFEA was large than that of the FDFEA.  Furthermore, the AFFEA needs more meshes for obtaining accurate results in high frequency region.  In the indoor acoustics analysis of room with sound absorption wall, the AFFEA needs the input of the acoustic impedance of the sound absorption wall, which was obtained from the FDFEA.  Analyses showed that subjected to the performance of the absorption material, the sound absorption effect was not good at low frequency region, but was greatly improved at high frequency region.  The FEFDA was also applied to simulate impedance experiment in this study and the results were found in good agreement with that obtained from the   one-dimensional predictions.

中文摘要	I
英文摘要	II
目錄	IV
圖目錄	VI
表目錄	VIII
第一章 緒論	1
1.1 前言	1
1.2 研究動機與目的	2
1.3 文獻回顧	3
1.4 研究內容	4
第二章 多孔材料與空間聲場之統御方程組	6
2.1 多孔材料統御方程組	6
2.1.1 應力、應變及位移	6
2.1.2 應力應變與應變能函數關係	8
2.1.3 動能及消散能量	9
2.1.4 Biot多孔線性彈性動態統御方程組	10
2.3 吸音係數	16
2.4 多孔彈性材料參數介紹	16
2.4.1 孔洞係數	17
2.4.2 多孔彈性材料參數與Biot彈性係數之關係	17
2.4.3 結構因子	18
2.4.4 消散係數	19
2.4.5 空氣之體積模數	20
2.5 空間聲場波動方程式	20
2.5.1 聲波運動方程式	21
2.5.2 聲波連續性方程式	22
2.5.3 聲波狀態方程式	23
2.5.4 聲波波動方程式	23
2.6 空間聲場之頻率響應	23
第三章 有限元素分析法	27
3.1 多孔彈性材料有限元素頻域分析法	27
3.1.1 多孔材料動態統御方程組	27
3.1.2 二維矩形有限元素	29
3.1.3 邊界條件	32
3.2 空間聲場有限元素分析法	33
3.2.1 二維空間聲場波動方程式	33
第四章 有限元素頻域分析結果	37
4.1 複數動態勁度	37
4.2 空間聲場聲響特性分析	41
4.2.1 無吸音層二維聲場之聲響特性	41
4.2.2 含吸音層二維聲場之聲響特性	51
4.3 網格數目之影響	57
4.4 吸音材料阻抗實驗模擬驗證	59
第五章 結論與未來展望	63
5.1 結論	63
5.2未來展望	64
參考文獻	66
符號索引	70
圖2-1：材料可穿透表面受均勻衝擊聲壓作用示意圖	11
圖2-2：燒結金屬銅材料的孔洞分佈圖	17
圖2-3：非黏滯性介質之微單元體	22
圖2-4：三維密閉空間聲場	24
圖3-1：多孔材料矩形元素示意圖	29
圖3-2：直角座標系多孔材料矩形元素尺寸圖	30
圖3-3：邊界條件示意圖	33
圖3-4：空間聲場矩形元素示意圖	34
圖3-5：直角座標系空間聲場矩形元素尺寸圖	35
圖4-1：矩形多孔材料一維模擬邊界示意圖	38
圖4-2：泡棉1之複數動態勁度(厚度0.016 m)	39
圖4-3：空氣層之複數動態勁度(厚度0.1 m)	40
圖4-4：無吸音層一維聲場模擬之網格及邊界條件圖	43
圖4-5：A點與B點之壓力頻率響應結果比較(一維模擬，無吸音層)	44
圖4-6：FEFDA與AFFEA之壓力頻率響應結果比較(一維模擬，無吸音層)	45
圖4-7：無吸音層二維聲場之網格及邊界條件圖	46
圖4-8：B點與C點之壓力頻率響應結果比較(二維模擬，無吸音層)	47
圖4-9：FEFDA與AFFEA之壓力頻率響應結果比較(二維模擬，無吸音層)	48
圖4-10：有吸音層一維聲場模擬之網格及邊界條件圖	51
圖4-11：FEFDA與AFFEA之壓力頻率響應結果比較(一維模擬，有吸音層)	52
圖4-12：有吸音層二維聲場之網格及邊界條件圖	53
圖4-13：FEFDA與AFFEA之壓力頻率響應結果比較(二維模擬，有吸音層)	54
圖4-14：不同網格於FEFDA模態頻率之影響分析(C點，實部)	57
圖4-15：不同網格於AFFEA模態頻率之影響分析(C點，實部)	58
圖4-16：泡棉1之動態勁度分析比較	60
圖4-17：泡棉2之動態勁度分析比較	61
圖4-18：泡棉1之吸音係數分析比較	62
圖4-19：泡棉2之吸音係數分析比較	62
表4-1：多孔彈性材料參數[26, 30]	38
表4-2：二維聲場之模態頻率	42
表4-3：模態頻率比較(無吸音層，A點)	49
表4-4：模態頻率比較(無吸音層，B點)	50
表4-5：模態頻率比較(無吸音層，C點)	50
表4-6：有無吸音層之聲壓比較(一維模擬，C點)	55
表4-7：有無吸音層之聲壓比較(二維模擬，C點)	56
表4-8：有無吸音層之聲壓比較(AFFEA，C點)	56
表4-9：不同網格數於AFFEA模態頻率之影響比較	58

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