摘要
本論文旨在研究發泡鋁板應用於噪音防治時之可行性，於文中探討當聲波入射至發泡鋁板時之波傳遞行為及量測發泡鋁板之音響特性，此外亦對發泡鋁板之材料性質及聲學性質進行分析，以充分瞭解發泡鋁板之特性。
本論文首先應用Biot多孔彈性理論為基礎，推導出多孔彈性材料的運動方程組，並藉由邊界條件，解得材料之透射損失。理論分析與實驗量測結果皆顯示，發泡鋁板於寬頻域中具有良好的隔音效果。本研究亦針對複合層之發泡鋁板進行實驗量測，結果顯示其透射損失較單層之發泡鋁板有更優異的隔音效果，於低頻處約增加5dB的透射損失，而於高頻處更超過10dB以上。
其次，本研究亦探討發泡鋁板的材料機械性質，將材料經由本文所建立之實驗分析量測，便可求得發泡鋁板之聲學性質及材料特性，藉此可瞭解發泡鋁板於防治噪音上之適用範圍。由本研究模式分析得知，若欲提昇發泡鋁板的隔音效果，針對隔離高頻噪音而言，係以增加材料厚度、密度及楊氏係數等最具成效，但對隔離低頻噪音而言效果並不顯著。此外材料厚度、密度越大共振頻率越低，而楊氏係數的增加則會將共振效應往高頻處移動。

ABSTRACT
The thesis focuses on aluminum porous board used in noise reduction. The experiment evaluates propagation of sound wave and examines acoustic characteristics of aluminum porous board when sound wave impinging on the aluminum porous board. Also, the material properties and acoustic properties of aluminum porous board are analyzed to help further understanding of aluminum porous board.
Biot`s poroelastic theory is essentially used to obtain the equation of motion of the elastic porous material, following the calculation of sound transmission loss via application of appropriate boundary condition. Supported by the theoretical analysis and measured data, the result in the thesis shows that aluminum porous board can provide well noise reduction throughout all frequency ranges. In addition, aluminum porous board lined with multi-panel structure, through analysis on sound transmission loss, proved better effect than single-paneled aluminum porous board in noise reducing. The difference is about 5dB in low frequency and more than 10dB in high frequency.
The studying of material mechanical properties of aluminum porous board is also included in the thesis, According to the database obtained in this thesis, acoustic properties and material properties of aluminum porous board can be worked out to estimate suitable aluminum porous board applied in noise reduction. The analysis suggests if higher noise reduction is required, one needs to thicken the aluminum porous board, or to increase density and Young`s modulus of the material, which results improvement in high frequency; but no effect in low frequency. Moreover, increasing material thickness and density will shift the resonance frequency to lower value; in addition, increasing Young`s modulus will move the resonance frequency to higher value.

目錄…………………………………………………………I
符號定義對照表……………………………………………IV
表目錄……………………………………………………VIII
圖目錄………………………………………………………IX
中文摘要…………………………………………………XIII
英文摘要…………………………………………………XIV
第一章 緒論…………………………………………………1
1.1 簡介與文獻回顧………………………………………1
1.2 研究動機與材料簡介…………………………………4
1.3 論文之組織與章節……………………………………5
第二章 多孔彈性材料之理論………………………………8
2.1 Biot多孔彈性材料理論………………………………8
2.1.1 應力與應變之關係…………………………………8
2.1.2 不考慮消散現象時的動態方程式…………………12
2.1.3 波傳遞方程式………………………………………16
2.1.4 考慮消散現象時之波傳遞方程式…………………18
2.1.5 波傳遞方程式之解…………………………………21
2.1.6 多孔彈性材料的邊界條件…………………………24
2.2 多孔彈性材料的應用…………………………………25
第三章 多孔彈性材料之材料係數………………………31
3.1 材料試驗………………………………………………31
3.2 孔洞係數………………………………………………34
3.3 流阻係數………………………………………………35
3.4 結構因子………………………………………………36
3.5 Biot理論之彈性係數…………………………………36
3.6 發泡鋁之聲學性質……………………………………38
3.7 計算範例………………………………………………39
3.7.1 範例一………………………………………………39
3.7.2 範例二………………………………………………40
第四章 發泡鋁板音響實驗之結果與討論………………50
4.1 單層板之隨機透射損失實驗…………………………52
4.1.1 單層板之隨機透射損失實驗量測一………………53
4.1.2 單層板之隨機透射損失實驗量測二………………56
4.2 複合板之隨機透射損失實驗量測……………………58
4.3 單層板之吸音係數實驗量測…………………………62
4.4 發泡鋁板材料係數之影響……………………………63
第五章 結論………………………………………………90
參考文獻……………………………………………………93
附錄A:透射損失計算範例…………………………………96
附錄B：Matlab程式………………………………………102

1. 陳雄文，“音響學會會刊：噪音管制法修正草案概敘“，中華民國音響學會，第七卷，第一期， 1999.
2. 白明憲，聲學理論與應用：主動式噪音控制，全華科技圖書公司，臺北市，1999.
3. 賴耿陽，環境噪音防止技術，復漢出版社，台南市，1990.
4. 黃忠良，噪音工學的基礎，復漢出版社，台南市，1985.
5. B.J. Smith, R.J. Peters, and S. Owen, Acoustics and Noise control, London, Longman, 1996.
6. 柴之隸，機械工程師手冊，中國機械工程學會編行，台北市，民國65.
7. 黃俊琦，金屬材料手冊，全華科技圖書公司，台北市，民國80.
8. 張印本、楊良太、嚴世明，ASTM金屬材料規格與對照，全華科技圖書公司，台北市，民國87.
9. 劉金源，水中聲學原理與應用，國立中山大學出版社，高雄市，1999.
10. L.E. Kinsler, A.R. Frey, A.B. Coppens and J.V. Sanders, Fundamentals of Acoustics, John Wiley & Sons, New York.1980.
11. R.D. Boer, “Highlights in The Historical Development of The Porous Media Theory : Toward A Consisent Macroscopic Theory,” Appl. Mech. Rev., 49(4), pp. 201-262, 1996.
12. 黃耀漢，多孔材料於吸振於吸音之應用，淡江大學機械工程研究所碩士論文，台北縣，1999.
13. M.A. Biot, “Theory of Elasticity and Consolidation for a Porous Anisotropic Solid,” J. Appl. Phy. 26(2), pp. 182-185, 1955
14. M.A. Biot, “Theory of Propagation of Elastic Wave in a Fluid-Saturated Porous Solid. I. Low-Frequency Range,” J. Acoust. Soc. Am. 28(2), pp. 168-178, 1956.
15. M.A. Biot, “Theory of Propagation of Elastic Wave in a Fluid-Saturated Porous Solid. II. Higher-Frequency Range,” J. Acoust. Soc. Am. 28(2), pp. 179-191, 1956.
16. M.A. Biot, “Generalized Theory of Acoustic Propagation in Porous Dissipative Media,” J. Acoust. Soc. Am. 34(9), pp. 1254-1264, 1962.
17. J.F. Allard, Achour Aknine and Claude Depollier,“Acoustical Properties of Partially Reticulated Foams with High and Medium Flow Resistance,”J. Acoust. Soc. Am. 79(6), pp. 1734-1740, 1986.
18. J.F. Allard, Michel Henry and Pavel Lemarinier,“Evaluation of the Characteristic dimensions for Porous Sound-Absorbing Materials,”J. Applied Physiics 77(1), pp. 17-20, 1995.
19. J.F. Allard, Propagation of Sound in Porous Media : Modeling Sound Absorbing Material, Elsevier Science Publishers , London, 1993.
20. J.F. Allard, Pavel Lemarinier and Denis Lafarge,“Dynamic Compressibility of Air in Porous Structures at Audible Frequencies,” J. Acoust. Soc. Am. 102(4), pp. 1995-2006, 1997.
21. A.Okuno, H. B. Kingsbury, “Dynamic Modulus of Poroelastic Materials,” J. Appl. Mech. 56, pp. 535-540, 1989.
22. K. Attenborough, “Acoustical Characteristics of Porous Materials,” Physics Reports 82 , pp. 179-227, 1982
23. J.S. Brown, “Connection Between Formation Factor for Electrical Resistivity and Fluid-Solid in Coupling Factor in Biot’s Equations for Acoustic Wave in Fluid-Filled Porous Media,” Geophysics 45(8) , pp. 1269-1275, 1980
24. J.S. Bolton and E.R. Green, “Normal Incidence Sound Transmission through Double-Panel Systems Lined with Relatively Stiff, Partially Reticulated Polyurethane Foam,” Applied Acoustics 39, pp. 23-51, 1993.
25. M.P. Norton, Fundamentals of Noise and Vibration Analysis for Engineers, Cambridge University Press, New York, 1989.
26. 宮紹華，“隔音及吸音於噪音防治工程之應用”，機械月刊，pp. 157-166，民國82年七月
27. J.S. Bolton, N.M. Shiau and Y.J. Kang, “Sound Transmission through Multi-Panel Structures Lined with Elastic Porous Materials,” J. of Sound and Vibration 191(3), pp. 317-347, 1996
28. K.B. Ginn, Application of B & K Equipment to Architectural Acoustics, Bruel & Kjar, Denmark, 1978.
29. L.L. Beranek, Acoustics, Acoustical Society of America, New York, 1988.
30. P.M. Morse and K.U. Ingard, Theoretical Acoustics, Princeton University Press, New Jersey, 1986.
1. Harold Lord, William S. Gatley, and H.A. Evensen, Noise Control For engineers, 虹橋出版社，臺北市，1985.
32. 曾富鑫，空心顆粒複合材料之機械性能與破壞分析，國立中山大學機械工程研究所碩士論文，高雄市，1994.
33. D. Hull, An Introduction to Composite Materials, Cambridge University Press, New York, 1985.
34. R. M. Christensen, Mechanics of Composite Materials, Krieger Publishers, Malabar, 1991.
35. A. D. Pierce, Acoustics, McGraw-Hill, New York, 1994
36. L. Cremer, M. Heckl, Structure-Borne Sound, Spring-Verlag, Berlin, 1988.
37. J. D. Webb, Noise Control in Industry, Halsted, New York, 1978.