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System No. U0002-3009201613325000
Title (in Chinese) 應用有限元素頻域聲學分析於施羅德擴散器的性能模擬
Title (in English) Performance Simulations of Schroeder Diffusers based on Finite Element Frequency Domain Acoustic Analysis
Other Title
Institution 淡江大學
Department (in Chinese) 機械與機電工程學系碩士班
Department (in English) Department of Mechanical and Electro-Mechanical Engineering
Other Division
Other Division Name
Other Department/Institution
Academic Year 104
Semester 2
PublicationYear 105
Author's name (in Chinese) 劉皓祥
Author's name(in English) Hao-Hsiung Liu
Student ID 602370529
Degree 碩士
Language Traditional Chinese
Other Language
Date of Oral Defense 2016-07-12
Pagination 76page
Committee Member advisor - Huoy-Shyi Tsay
co-chair - 柯德祥
co-chair - 李經綸
Keyword (inChinese) 有限元素頻域分析
吸音係數
擴散係數
吸音泡棉
施羅德擴散器
聆聽室
Keyword (in English) Finite Element Frequency Domain Analysis
Sound Absorption Coefficient
Diffusion Coefficient
Acoustic Foam
Schroeder Diffuser
Listening Room
Other Keywords
Subject
Abstract (in Chinese)
本研究應用多孔介質二維有限元素頻域分析計算聆聽室的頻率響應。分析驗證吸音泡棉的吸音係數與施羅德擴散器的極響應及擴散係數,並探討結合吸音泡棉與施羅德擴散器於聆聽室頻率響應的影響。
本研究首先應用有限元素頻域分析與雙麥克風法計算吸音泡棉的吸音係數,並與一維理論解進行比較,驗證於聆聽室附加吸音泡棉時亦可正確獲得吸音係數。接著應用有限元素頻域分析繪製500 Hz施羅德擴散器的極響應圖並驗證其擴散效果。從極響應圖中可觀察出七槽施羅德擴散器的擴散效果最佳,各個單槽均有顯著的集中反射現象,擴散效果差。最後本研究應用邊界條件與均佈脈衝聲壓模擬聆聽室的頻率響應,分析結合吸音泡棉與施羅德擴散器對聆聽室頻率響應的影響。結果顯示在聆聽室附加三個施羅德擴散器較附加一個施羅德擴散器的擴散效果為佳。結合吸音泡棉與施羅德擴散器後,聆聽點各三分之一倍頻帶的位移振幅皆顯著下降,顯見吸音泡棉的吸音效果。惟擴散器與吸音泡棉的結合使用,須考量適切的聆聽頻率響應需求予以適當的設計。
Abstract (in English)
The two-dimensional finite element frequency domain analysis (FEFDA) of a porous medium is used to calculate the frequency responses of a listening room in this study.  Sound absorption coefficient of acoustic foam and polar plots as well as diffusion coefficient of Schroeder diffuser are analyzed and validated.  The effects of acoustic foams and Schroeder diffusers on the frequency responses of a listening room are studied.

FEFDA and two-microphone method are applied to calculate the sound absorption coefficient of acoustic foam and the results are further compared with the one-dimensional analytical result.  It is found that the correct sound absorption coefficient can be obtained while the acoustic foam is applied to the listening room.  Polar plots of 500 Hz Schroeder diffuser are prepared using the FEFDA and the related diffusion coefficients are verified.  Results show that the 7-slot Schroeder diffuser has better diffusion effect and single-slot diffusers have worse diffusive performance due to the concentrated reflections.  Finally, the impulsive pressure and suitable boundary conditions are applied to study the frequency responses of a listening room.  The influences of the combination of the acoustic foams and Schroeder diffusers are explored.   It is learned that a better diffusion performance is obtained when applying three Schroeder diffusers as compared with that has only one diffuser.  The decreasing of the displacement amplitude at each one-third octave band shows that the acoustic foams have significant sound adsorbing effect.  However, an appropriate frequency response should be taken into consideration while providing the treatments of acoustic foams and Schroeder diffusers to a listing room.
Other Abstract
Table of Content (with Page Number)
目  錄
中文摘要	I
英文摘要	II
目  錄	IV
圖目錄	VI
表目錄	VIII
符號索引	X
第一章 緒論	1
1.1 前言	1
1.2 研究動機	1
1.3 文獻回顧	2
1.4 研究內容	4
第二章 多孔介質結構理論與有限元素頻域分析	6
2.1 多孔彈性理論	6
2.1.1 固、流體應力與應變關係	6
2.1.2 動能及耗損能	8
2.1.3多孔彈性介質之動態統御方程組	9
2.2 多孔介質材料參數	9
2.2.1 孔洞係數	9
2.2.2 多孔介質有效密度	9
2.2.3 結構因子	10
2.2.4 動態消散係數	10
2.2.5 空氣體積模數	11
2.2.6 彈性係數與材料係數之關係	11
2.3 上表面可穿透吸音材料的脈衝響應	12
2.4 動態勁度、阻抗與吸音係數	16
2.5多孔介質有限元素頻域分析	17
第三章 聲學理論與施羅德擴散器	22
3.1聲學理論介紹	22
3.1.1波與聲波	22
3.1.2聲音基本參數	24
3.1.3吸音係數	25
3.1.4擴散係數與散射係數	26
3.2施羅德擴散器	29
3.2.1基本理論	29
3.2.2設計方法	31
3.3聆聽室之設計	32
第四章 結果與討論	36
4.1吸音泡棉驗證與分析	36
4.2施羅德擴散器驗證與分析	39
4.3聆聽室頻率響應分析	62
第五章 結論與未來展望	69
5.1 結論	69
5.2 未來展望	71
參考文獻	73
 
圖目錄
圖2-1  含飽和流體之多孔吸音材料示意圖	12
圖2-2  多孔介質四邊形元素直角座標系示意圖	17
圖2-3  多孔介質正方形元素自然座標系示意圖	18
圖3-1  縱波(a)與橫波(b)示意圖	23
圖3-2  阻抗管內麥克風1和2擺放位置示意圖	25
圖3-3  散射的定義示意圖	28
圖3-4  一維施羅德擴散器	30
圖3-5  一維施羅德擴散器(N0=7)橫截面圖	30
圖3-6  二維施羅德擴散器	31
圖3-7  喇叭與聆聽者的關係	33
圖3-8  較佳的聆聽室共振頻率圖	35
圖3-9  較差的聆聽室共振頻率圖	35
圖4-1  吸音泡棉示意圖	36
圖4-2  吸音泡棉有限元素圖	37
圖4-3  吸音泡棉吸音係數的理論與FEFDA結果比較	38
圖4-4  吸音泡棉外加空氣層邊界設定示意圖	38
圖4-5  吸音泡棉外加空氣層的吸音係數	39
圖4-6  各槽元素圖	40
圖4-7  0.075  0.049 共振頻率圖	41
圖4-8  0.075  0.098 共振頻率圖	42
圖4-9  0.075  0.196 共振頻率圖	42
圖4-10  平面元素圖(Sn為0)	43
圖4-11  一槽擴散器元素圖(Sn為1,槽深0.049 m)	44
圖4-12  一槽擴散器元素圖(Sn為2,槽深0.098 m)	44
圖4-13  一槽擴散器元素圖(Sn為4,槽深0.196 m)	45
圖4-14  七槽擴散器元素圖	45
圖4-15  37個量測節點圖	46
圖4-16  0度1 m施力點與2 m量測點的位移時域圖	47
圖4-17  0度施力y方向極響應圖	49
圖4-18  -30度施力y方向極響應圖	50
圖4-19  -60度施力y方向極響應圖	51
圖4-20  0度施力y方向1/3倍頻帶極響應圖	54
圖4-21  -30度施力y方向1/3倍頻帶極響應圖	55
圖4-22  -60度施力y方向1/3倍頻帶極響應圖	56
圖4-23  0度施力y方向極響應圖(扣除平面響應)	57
圖4-24  -30度施力y方向極響應圖(扣除平面響應)	58
圖4-25  -60度施力y方向極響應圖(扣除平面響應)	59
圖4-26  0度施力y方向1/3倍頻帶極響應圖(扣除平面響應)	60
圖4-27  -30度施力y方向1/3倍頻帶極響應圖(扣除平面響應)	61
圖4-28  -60度施力y方向1/3倍頻帶極響應圖(扣除平面響應)	62
圖4-29  聆聽室與附加延伸空間聆聽室的元素圖	63
圖4-30  聆聽室與附加延伸空間後的共振頻率	64
圖4-31  3  5 房間(a)與附加延伸空間(b)的共振頻率	64
圖4-32  聆聽室附加施羅德擴散器元素圖	65
圖4-33  聆聽室結合吸音泡棉與施羅德擴散器元素圖	66
圖4-34  聆聽室附加一個施羅德擴散器實照圖	66
圖4-35  聆聽室附加三個施羅德擴散器實照圖	67
圖4-36  1.2 吸音泡棉擺設實體圖	67
圖4-37  聆聽室的1/3倍頻帶位移振幅比較圖	68


 
表目錄
表3-1  房間共振頻率	34
表4-1  吸音泡棉與空氣的材料參數	37
表4-2  三分之一倍頻帶之中心頻率與頻寬	52
References
參考文獻
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2.	M. R. Schroeder, “Diffuse Sound Reflection by Maximum-Length Sequences”, The Journal of the Acoustical Society of America, Vol. 57 , No. 1, pp. 149-50, 1975.
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