本研究執行纖維吸音材料動態流阻與聲響性質之模擬分析與量測；研究中使用多孔彈性理論模擬動態流阻產生之吸音係數，並與雙麥克風阻抗管量測之吸音係數進行比較探討。
本文首先運用Navier-Stokes流體運動方程式於拉普拉斯域及邊界條件設定下進行動態平行流阻之推導，其次使用透氣試驗法、雙厚度法及無響室法量測玻璃纖維與岩棉纖維吸音材料的流阻，並與Tarnow之動態平行與垂直流阻模擬結果進行比較。續而應用雙麥克風阻抗管量測兩種纖維吸音材料之聲響性質，並探討於材料厚度及密度改變下對聲響性質如音響阻抗、複數動態勁度、吸音係數等之影響。之後再藉由Biot多孔彈性理論推導上表面可穿透之吸音平板之複數動態勁度、音響阻抗及吸音係數。並據以探討應用材料厚度、密度及動態流阻量測值所模擬之吸音係數與量測吸音係數之差異。
由研究結果顯示纖維材料之間距、排列方式、密度、厚度等皆是影響動態流阻與聲響性質之重要因素。本文推導之平行流阻與三種不同方式量測之流阻皆落於Tarnow推導之平行與垂直流阻預估值之間，三種量測法中以雙厚度法較適合一般實驗室量測使用。由流阻量測值及材料參數所衍生之吸音係數預估值，於中低頻域與雙麥克風阻抗管量測之吸音係數結果相符，而於中高頻域時則與阻抗管吸音係數量測結果互有差異但趨勢相符，其中以無響室法所模擬之吸音係數結果較接近於量測結果。

In this thesis, dynamic flow resistance and acoustic properties of fibrous sound absorbing materials are simulated and measured. In the study, the poroelastic theory is used to simulate the dynamic flow resistance extending sound absorption coefficient, and carries two-microphone impedance tube measurement on the comparison.
During the study, the dynamic parallel flow resistance is first derived from using Navier-Stokes equation in Laplace domain with specified boundary conditions. Secondary, flow resistances of fiberglass and rock wool sound absorbing materials are measured using air permeability test method, two-thickness method, and anechoic chamber method, then, the measured results are compared with that resulted from Tarnow’s parallel and perpendicular dynamic flow resistance simulations. Thereafter, acoustic properties of two kind of fibrous absorbing materials are measured by two-microphone impedance tube method, and the influences of material thickness and density on the acoustic properties such as acoustical impedance, complex dynamic stiffness, and sound absorption coefficient are also discussed. Afterward, complex dynamic stiffness, acoustical impedance, and sound absorption coefficient for the fibrous absorbing material with a permeable upper surface are derived using Biot’s poroelastic theory. Accordingly, the differences between the sound absorption coefficient simulated with the use of thickness, density, dynamic flow resistance, and that measured are discussed.
It is learned that the spacing of fiber, fiber arrangement, density, and thickness are key factors for affecting the dynamic flow resistance and acoustical properties. In the study, it is found the simulated parallel flow resistance and the flow resistances measured by three measuring ways fall in between the values predicted by Tarnow’s parallel and perpendicular dynamic flow resistance simulations. Two-thickness method is superior to the other two kinds of measuring ways in Labs. The sound absorption coefficients simulated by applying the measured flow resistance and material properties are agree with that measured by two-microphone impedance tube method, in the low frequency region. And in the high frequency region, the simulated values have the differences with the measuring results but both have the same tendency. The sound absorption coefficients predicted by the results of the anechoic chamber method is proved much closer to the measured results.

目  錄
中文摘要 ------------------------------------------------------------------------- I
英文摘要 ----------------------------------------------------------------------- III
目    錄 ------------------------------------------------------------------------ V
圖表索引 ----------------------------------------------------------------------- IX
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 -------------------------------------------------------------- 4
1.4 研究內容 -------------------------------------------------------------- 8
第二章 纖維吸音材料之材料參數與流阻 ------------------------------- 10
2.1 纖維吸音材料孔洞係數 ------------------------------------------ 11
2.2 纖維吸音材料流阻 ------------------------------------------------ 12
2.3 平行流阻與垂直流阻 --------------------------------------------- 16
2.3.1 平行流阻 ---------------------------------------------------- 16
2.3.2 垂直流阻 ---------------------------------------------------- 17
2.4 纖維吸音材料之纖維排列 --------------------------------------- 18
2.5 纖維吸音材料之材料參數 --------------------------------------- 22
2.5.1 纖維吸音材料之孔洞係數 ------------------------------- 22
2.5.2 纖維吸音材料之纖維質量與材料密度 ---------------- 23
2.5.3 纖維吸音材料之纖維直徑 ------------------------------- 23
2.5.4 纖維吸音材料之剪力模數 ------------------------------- 23
2.6 多孔材料之材料參數 --------------------------------------------- 25
第三章 動態流阻之量測 ---------------------------------------------------- 28
3.1 流阻 ------------------------------------------------------------------ 28
3.2 流阻之量測 --------------------------------------------------------- 30
3.2.1 透氣試驗法 ------------------------------------------------- 30
3.2.1.1 量測原理與方法 ----------------------------------- 30
3.2.1.2 量測步驟與注意事項 ----------------------------- 32
3.2.1.3 量測結果與討論 ----------------------------------- 33
3.2.2 阻抗管雙厚度法 ------------------------------------------- 33
3.2.2.1 量測原理與方法 ----------------------------------- 33
3.2.2.2 量測設備與注意事項 ----------------------------- 35
3.2.2.3 量測結果與討論 ----------------------------------- 38
3.2.3 無響室法 ---------------------------------------------------- 44
3.2.3.1 量測原理與方法 ----------------------------------- 44
3.2.3.2 量測設備與注意事項 ----------------------------- 46
3.2.2.3 量測結果與討論 ----------------------------------- 47
3.3 動態流阻之量測與模擬值比較 --------------------------------- 50
第四章 纖維吸音材料之聲響性質 ---------------------------------------- 60
4.1 吸音係數 ------------------------------------------------------------ 60
4.2 吸音係數量測 ------------------------------------------------------ 62
4.2.1 量測原理與方法 ------------------------------------------- 62
4.2.2 量測設備與架設 ------------------------------------------- 63
4.2.3 量測步驟與注意事項 ------------------------------------- 64
4.2.4 纖維吸音材料參數 ---------------------------------------- 66
4.2.5 量測結果 ---------------------------------------------------- 66
4.3 聲響性質 ------------------------------------------------------------ 70
4.3.1 音響阻抗 ---------------------------------------------------- 70
4.3.2 動態勁度 ---------------------------------------------------- 76
第五章 纖維吸音材料吸音係數比較 ------------------------------------- 81
5.1 多孔彈性材料之位移及應力函數 ------------------------------ 81
5.2 表面可穿透吸音平板之吸音係數 ------------------------------ 85
5.3 吸音係數比較 ------------------------------------------------------ 86
第六章 結論與未來展望 ---------------------------------------------------- 92
6.1 結論 ------------------------------------------------------------------ 92
6.2 未來展望 ------------------------------------------------------------ 95
附錄A 纖維吸音材料之材料性質量測 ---------------------------------- 97
A.1 孔洞率量測 -------------------------------------------------------- 97
A.2 質量量測 ---------------------------------------------------------- 101
A.3 纖維直徑量測 ---------------------------------------------------- 102
A.4 剪力模數量測 ---------------------------------------------------- 106
A.5 材料試片 ---------------------------------------------------------- 109
附錄B FX 3300-III透氣試驗儀 ------------------------------------------- 113
B.1 設備規格 ---------------------------------------------------------- 113
B.2 量測數據 ---------------------------------------------------------- 114
附錄C SD-390頻譜分析儀器 --------------------------------------------- 115
C.1 儀器設定 ---------------------------------------------------------- 115
C.2 量測數據 ---------------------------------------------------------- 118
參考文獻 ---------------------------------------------------------------------- 119
符號索引 ---------------------------------------------------------------------- 123 
圖索引
圖2-1 纖維吸音材料之纖維平行排列示意圖 -------------------------- 11
圖2-2 纖維吸音材料邊界限制條件示意圖 ----------------------------- 13
圖2-3 纖維吸音材料孔洞示意圖 ----------------------------------------- 15
圖2-4 纖維端面三角形排列示意圖 -------------------------------------- 19
圖2-5 纖維吸音材料流阻模擬值比較(實部) ---------------------------- 21
圖2-6 纖維吸音材料流阻模擬值比較(虛部) ---------------------------- 21
圖3-1 透氣度試驗儀(FX 3300-III) ----------------------------------------- 31
圖3-2 雙厚度法待測試片示意圖 ----------------------------------------- 34
圖3-3 雙麥克風阻抗管量測設備示意圖 -------------------------------- 37
圖3-4 雙麥克風阻抗管量測設備圖 -------------------------------------- 37
圖3-5 R040之表面音響阻抗(實部) ---------------------------------------- 39
圖3-6 R040之表面音響阻抗(虛部) ---------------------------------------- 39
圖3-7 R040之表面特徵阻抗(實部) ---------------------------------------- 40
圖3-8 R040之表面特徵阻抗(虛部) ---------------------------------------- 40
圖3-9 R040特徵阻抗實部與頻率流阻比關係圖(0.5&1 cm) ---------- 41
圖3-10 R040特徵阻抗實部與頻率流阻比關係圖(1&2 cm) ----------- 41
圖3-11 R040特徵阻抗實部與頻率流阻比關係圖(2&4 cm) ----------- 42
圖3-12 R040之動態流阻(0.5&1 cm)(實部) ------------------------------- 42
圖3-13 R040之動態流阻(1&2 cm)(實部) --------------------------------- 43
圖3-14 R040之動態流阻(2&4 cm)(實部) --------------------------------- 43
圖3-15 吸音海綿尺寸 ------------------------------------------------------- 45
圖3-16 吸音箱內部泡棉分佈圖 ------------------------------------------- 46
圖3-17 無響室法之量測設備示意圖 ------------------------------------- 48
圖3-18 R040之表面音響阻抗值(0.006 m)(實部) ------------------------ 48
圖3-19 無試片之表面音響阻抗值(實部) --------------------------------- 49
圖3-20 R040之動態流阻(0.006 m)(實部) --------------------------------- 49
圖3-21 R040量測與模擬流阻之比較 ------------------------------------- 51
圖3-22 R060量測與模擬流阻之比較 ------------------------------------- 51
圖3-23 R080量測與模擬流阻之比較 ------------------------------------- 52
圖3-24 R100量測與模擬流阻之比較 ------------------------------------- 52
圖3-25 F032量測與模擬流阻之比較 ------------------------------------- 53
圖3-26 F048量測與模擬流阻之比較 ------------------------------------- 53
圖3-27 F100量測與模擬流阻之比較 ------------------------------------- 54
圖3-28 R040動態與靜態流阻比 ------------------------------------------- 54
圖3-29 R060動態與靜態流阻比 ------------------------------------------- 55
圖3-30 R080動態與靜態流阻比 ------------------------------------------- 55
圖3-31 R100動態與靜態流阻比 ------------------------------------------- 56
圖3-32 F032動態與靜態流阻比 ------------------------------------------- 56
圖3-33 F048動態與靜態流阻比 ------------------------------------------- 57
圖3-34 F100動態與靜態流阻比 ------------------------------------------- 57
圖4-1 玻璃纖維密度於吸音係數之影響(厚度0.0254 m) ------------- 68
圖4-2 玻璃纖維密度於吸音係數之影響(厚度0.0508 m) ------------- 68
圖4-3 岩棉密度於吸音係數之影響(厚度0.0254 m) ------------------- 69
圖4-4 岩棉密度於吸音係數之影響(厚度0.0508 m) ------------------- 69
圖4-5 玻璃纖維密度於音響阻抗之影響(厚度0.0254 m)(實部) ----- 72
圖4-6 玻璃纖維密度於音響阻抗之影響(厚度0.0254 m)(虛部) ----- 72
圖4-7 玻璃纖維密度於音響阻抗之影響(厚度0.0508 m)(實部) ----- 73
圖4-8 玻璃纖維密度於音響阻抗之影響(厚度0.0508 m)(虛部) ----- 73
圖4-9 岩棉密度於音響阻抗之影響(厚度0.0254 m)(實部) ----------- 74
圖4-10 岩棉密度於音響阻抗之影響(厚度0.0254 m)(虛部) ---------- 74
圖4-11 岩棉密度於音響阻抗之影響(厚度0.0508 m)(實部) ---------- 75
圖4-12 岩棉密度於音響阻抗之影響(厚度0.0508 m)(虛部) ---------- 75
圖4-13 玻璃纖維密度於動態勁度之影響(厚度0.0254 m)(實部) ---- 77
圖4-14 玻璃纖維密度於動態勁度之影響(厚度0.0254 m)(虛部) ---- 77
圖4-15 玻璃纖維密度於動態勁度之影響(厚度0.0508 m)(實部) ---- 78
圖4-16 玻璃纖維密度於動態勁度之影響(厚度0.0508 m)(虛部) ---- 78
圖4-17 岩棉密度於動態勁度之影響(厚度0.0254 m)(實部) ---------- 79
圖4-18 岩棉密度於動態勁度之影響(厚度0.0254 m)(虛部) ---------- 79
圖4-19 岩棉密度於動態勁度之影響(厚度0.0508 m)(實部) ---------- 80
圖4-20 岩棉密度於動態勁度之影響(厚度0.0508 m)(虛部) ---------- 80
圖5-1 材料可穿透表面受均勻衝擊聲壓作用示意圖 ----------------- 86
圖5-2 R040量測與模擬吸音係數之比較 -------------------------------- 88
圖5-3 R060量測與模擬吸音係數之比較 -------------------------------- 89
圖5-4 R080量測與模擬吸音係數之比較 -------------------------------- 89
圖5-5 R100量測與模擬吸音係數之比較 -------------------------------- 90
圖5-6 F032量測與模擬吸音係數之比較 --------------------------------- 90
圖5-7 F048量測與模擬吸音係數之比較 --------------------------------- 91
圖5-8 F100量測與模擬吸音係數之比較 --------------------------------- 91
圖A-1 鑚床機 ----------------------------------------------------------------- 98
圖A-2 中空圓柱型切割刀具 ----------------------------------------------- 98
圖A-3 玻璃纖維吸音材料 -------------------------------------------------- 99
圖A-4 岩棉纖維吸音材料 -------------------------------------------------- 99
圖A-5 微量天平儀器 ------------------------------------------------------ 101
圖A-6 光學顯微鏡 --------------------------------------------------------- 103
圖A-7 光學顯微鏡儀器量測設備 --------------------------------------- 103
圖A-8 纖維吸音材料排列分佈情形 ------------------------------------ 104
圖A-9 纖維吸音材料纖維直徑觀測圖(500倍) ------------------------ 104
圖A-10 纖維吸音材料纖維直徑觀測圖(1000倍) --------------------- 105
圖A-11 纖維吸音材料之剪力模數量測示意圖 ----------------------- 107
圖A-12 纖維吸音材料承受剪力之位移及角度變化圖 -------------- 107
圖A-13 玻璃纖維吸音材料承受剪力變化圖 -------------------------- 108
圖A-14 岩棉纖維吸音材料承受剪力變化圖 -------------------------- 108
圖A-15 F032阻抗管雙厚度法材料試片 -------------------------------- 110
圖A-16 R040阻抗管雙厚度法材料試片 -------------------------------- 110
圖A-17 F032阻抗管無響室法材料試片(厚度0.006 m) -------------- 110
圖A-18 R040阻抗管無響室法材料試片(厚度0.006 m) -------------- 110
圖A-19 F032雙麥克風阻抗管法材料試片(厚度0.0254 m) ---------- 111
圖A-20 F032雙麥克風阻抗管法材料試片(厚度0.0508 m) ---------- 111
圖A-21 R040雙麥克風阻抗管法材料試片(厚度0.0254 m) ---------- 111
圖A-22 R040雙麥克風阻抗管法材料試片(厚度0.0508 m) ---------- 112
圖B-1 量測數據擷取畫面 ------------------------------------------------ 114
圖C-1 數據擷取設定 ------------------------------------------------------ 115
圖C-2 數據分析設定 ------------------------------------------------------ 116
圖C-3 轉移函數實部設定 ------------------------------------------------ 117
圖C-4 轉移函數虛部設定 ------------------------------------------------ 117
圖C-5 量測數據擷取畫面 ------------------------------------------------ 118
 
表索引
表2-1 玻璃纖維吸音材料之材料參數表 -------------------------------- 24
表2-2 岩棉纖維吸音材料之材料參數表 -------------------------------- 24
表3-1 纖維吸音材料之透氣性量測數據 -------------------------------- 33
表3-2 玻璃纖維吸音材料之流阻值比較 -------------------------------- 58
表3-3 岩棉纖維吸音材料之流阻值比較 -------------------------------- 59
表4-1 玻璃纖維吸音材料待測試片之厚度與密度 -------------------- 66
表4-2 岩棉纖維吸音材料待測試片之厚度與密度 -------------------- 66
表5-1 纖維吸音材料之材料參數表 -------------------------------------- 88
表A-1 孔洞係數量測之試片規格 --------------------------------------- 100
表A-2 F048之纖維體積與孔洞係數 ------------------------------------ 100
表A-3 R100之纖維體積與孔洞係數 ------------------------------------ 100
表A-4 玻璃纖維吸音材料之質量量測值 ------------------------------ 101
表A-5 岩棉纖維吸音材料之質量量測值 ------------------------------ 102
表A-6 玻璃纖維直徑 ------------------------------------------------------ 105
表A-7 岩棉纖維直徑 ------------------------------------------------------ 105
表A-8 玻璃纖維吸音材料之剪力模數 --------------------------------- 109
表A-9 岩棉纖維吸音材料之剪力模數 --------------------------------- 109
表B-1 透氣試驗儀量測探頭及流速量測範圍 ------------------------- 114

參考文獻
1.	Biot M. A., “General theory of three dimensional consolidation,” J. Appl. Phys., 12, pp.155-164, 1941.
2.	Biot M. A., “Theory of propagation of elastic waves in a fluid saturated porous solid-I : low-frequency range,” J. Acoust. Soc. Am., 28(2), pp.168-178, 1956.
3.	Biot M. A., “Theory of propagation of elastic waves in a fluid saturated porous solid-II : higher-frequency range,” J. Acoust. Soc. Am., 28(2), pp.179-191, 1956.
4.	Biot M. A. and Willis D.G., “The elastic coefficients of the theory of consolidation,” J. Appl. Mech. (Trans ASME), 24, pp.594-601, 1957.
5.	Biot M. A., “Generalized theory of acoustic propagation in porous dissipative media,” J. Acoust. Soc. Am., 34(9), pp.1254-1264, 1962.
6.	Biot M. A., “General solutions of the equations of elasticity and consolidation for a porous material,” J. Appl. Mech. (Trans ASME), 23, pp.91-96, 1965.
7.	Cremer L. and Muller H. A., “Principles and applications of room acoustics,” J. Acoust. Soc. Am., 76(4), pp.1277-1285, 1984.
8.	Voronina N., “Acoustic properties of fibrous materials,” Applied   Acoustics, 42(2), pp.165-174, 1994.
9.	Delany M. E. and Bazley E. N., “Acoustical properties of fibrous materials,” Applied Acoustics, 3, pp.105-116, 1970.
10.	Smith C. D. and Parrott T. L., “Comparison of three methods for measuring acoustic properties of bulk materials,” J. Acoust. Soc. Am., 74(5), pp.1577-1582, 1983.
11.	Woodcock R. and Hodgson M., “Acoustic methods for determining the effective flow resistivity of fibrous materials,” Journal of Sound and Vibration, 153(1), pp.186-191, 1992.
12.	Ingard K. U. and Dear T. A., “Measurement of acoustic of flow resistance,” Journal of Sound and Vibration, 103(4), pp.567-572, 1985.
13.	Bies D. A. and Hansen C. H., “Flow resistance information for acoustical design,” Applied Acoustics, 13(5), pp.357-391, 1980.
14.	Ballagh K. O., “Acoustical properties of wool,” Applied Acoustics, 48(2), pp.101-120, 1996.
15.	Davis A. M. J. and James D. F., “Slow flow through a model fibrous porous medium,” International Journal of Multiphase Flow, 22(5), pp. 969-989, 1996.
16.	Liew T. P. and Conder J. R., “Fine mist filtration by wet filters-I. liquid saturation and flow resistance of fibrous filters,” Journal of Aerosol Science, 16(6), pp.497-509, 1985.
17.	Allard J. F., “Propagation of sound in porous media modeling sound absorbing material,” Elsevier Science Publisher, England, 1993.
18.	Kirby R. and Cummings A., “Prediction of the bulk acoustic properties of fibrous materials at low frequencies,” Applied Acoustics, 56, pp. 101-125, 1999.
19.	Viggo Tarnow, “Calculation of the dynamics air flow resistivity of fiber materials,” J. Acoust. Soc. Am., 102(3), pp.1680-1688, 1997.
20.	Viggo Tarnow, “Airflow resistivity of models of fibrous acoustic materials,” J. Acoust. Soc. Am., 100(6), pp.3706-3713, 1996.
21.	Sangani A. S. and Yao C, “Transport processes in random arrays of cylinders. II,” Phys. Fluids, 31, pp.2435-2444, 1998.
22.	Huszty D., Illenyi A., and Vass Gy., “Equipment for measuring the flow-resistance of porous and fibrous materials,” Applied Acoustics, 5(1), pp.1-14, 1972.
23.	Yang T. L., Chianq D. M., and Chen R., “Development of a novel porous laminated composite material for high sound absorption,” Journal of Vibration and Control, 7(5), pp.675-698, 2001.
24.	Attenborough K., “On the acoustic slow wave in air-filled granular media,” J. Acoust. Soc. Amer, 81, pp.93-102, 1987.
25.	Allard J. F., Depollier C. and Aknine A., “Acoustical properties of partially reticulater foams with high and medium flow resistance,” J. Acoust. Soc. Amer, 79, pp.1734-40, 1986.
26.	Allard J. F., Depollier Claude, Rebillard Pascal, Walter Lauriks and Cops Andre., “Inhomogeneous Biot wave in layered media,” J. Appl. Physics, 66, pp.2278-2284, 1989.
27.	Zwikker C. and Kosten C. W., “Sound absorbing materials,” Elasevier, 1949.
28.	Tsay H. S. and Kingsbury H. B., “Influence of inertia and dissipative forces on the dynamic response of poroelastic materials,” Int. J. Solids Structure, 29(5), pp.641-652, 1992.
29.	Tsay H. S. and Yeh F. H., “Dynamic Response of Poroelastic Slab,” The   National Conf. On Theoretical and Appl. Mech., Taipei, Taiwan, R.O.C., pp.1005-1012, 1993.
30.	蔡慧駿，葉豐輝，“多孔吸音板音響阻抗及吸音係數分析研究，” 中華民國音響學會第十二屆學術研討會論文集，pp.162-169，台北(88.12)。
31.	Kirby R. and Cummings A., “Prediction of the bulk acoustic properties of fibrous materials at low frequencies,” Applied Acoustics, 56, pp. 101-125, 1999.
32.	Picard M. A. and Solana P. etc., “A method of measuring the dynamic flow resistance and the acoustic measurement of the effective static flow resistance in stratified rockwool samples,” Journal of Sound and Vibration, 216(3), pp.495-505, 1998.
33.	Minqzhang R. and Jacobsen F., “Method of measuring the dynamic flow resistance and reactance of porous materials,” Applied Acoustics, 39(4), pp.265-276, 1993.
34.	Chung J. Y. and Blaser D. A., “Transfer function of measuring acoustic intensity in a duct system with flow,” J. Acoust. Soc. Am., 68(6), pp. 1570-1577, 1980.
35.	Chung J. Y. and Blaser D. A., “Transfer function of measuring in-duct acoustic properties em dash 2. experiment,” J. Acoust. Soc. Am., 68(3), pp.914-921, 1980.
36.	Chung J. Y. and Blaser D. A., “Transfer function technique for determining the acoustic characteristics of duct systems with flow,” Proceeding-International Conference on Noise Control Engineering, pp. 901-908, 1978.