臺灣博碩士論文加值系統

本研究探討多孔彈性材料於不同邊界限制下之吸音效果。不須透過吸音材料表面空氣層驅動多孔彈性材料，研究中直接藉由一施於材料表面的衝擊壓力，應用拉普拉斯域有限元素分析法於拉普拉斯域中直接擷取吸音材料之表面音響阻抗再經轉換求得吸音係數。
研究中首先針對不同厚度之多孔吸音平板探討滾動及固定邊界限制於多孔材料吸音特性之影響。分析時除使用拉普拉斯域二維與三維有限元素分析法詳細探討外，也應用一維理論解及雙麥克風阻抗量測完成結果比較驗證。阻抗管驗證結果顯示試驗時吸音平板試片邊界為一彈性變動邊界，隨著平板厚度或頻率之增加漸而由滾動驅向固定邊界限制；也顯示邊界限制對多孔材料吸音係數值確有顯著之影響。
於獲得實驗與分析之一致性後，本研究續而應用拉普拉斯域有限元素法探討邊界限制於表面皺折多孔吸音板吸音係數的影響。研究中分別模擬並獲得二維對稱角錐條型、不對稱角錐條型、橢圓條型與三維金字塔型表面皺折多孔吸音板最佳吸音外形尺寸。在同材質及體積之比較基礎下，可發現角錐條型低頻時之吸音效果較金字塔型為佳而中高頻時則反之。而不對稱角錐條型之角錐尖端側移確有助於提昇吸音係數頻域的平均值。至於橢圓條型者其吸音效果較集中於一特定範圍，而其所涵蓋之頻率範圍較角錐條型為廣。

The influence of edge restraints on the sound absorption coefficient of porous materials is studied in this thesis. Instead of the use of air for actuating the porous materials, a uniformly distributed impulsive pressure is directly applied on the surface of the porous materials in the study. Through the Laplace domain finite element method, the surface acoustic impedance of porous materials is directly obtained and the sound absorption coefficient is calculated accordingly.
The sound absorption characteristics of porous plates with different thickness subjected to the influence of rolling as well as fixed boundary restraints are first studied. Two and three dimensional Laplace domain finite element methods are used for analyses, then one dimensional theoretical solutions and two microphones impedance tube experiments are used for verifications. Results show the increase of thickness or frequency will change the restraint of specimens gradually from rolling to fix. During the changing of restraint, the sound absorption coefficient is remarkably affected.
The Laplace domain finite element method is further applied for study the corrugated porous plates subjected to the influence of boundary restraints. Porous plate with symmetric and asymmetric wedge, elliptic, and pyramid surfaces are analyzed and optimal dimensions with the best sound absorption performance are also acquired. On the basis of same material and volume, it is found plates with wedge surface are superior to plates with pyramid surface in low frequency region, but on the contrary in mid- and high frequency regions. Moving the wedge tip of plates with asymmetric wedge could improve the sound absorption coefficient. The sound absorption frequency range of plates with elliptic surface is concentrated in a certain frequency band.

中文摘要 Ⅰ
英文摘要 Ⅱ
目錄 Ⅳ
圖目錄 Ⅵ
表目錄 Ⅸ
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 論文之構成 3
第二章 基本理論與材料參數 5
2.1 Biot多孔彈性理論簡介 6
2.1.1 應力、應變與位移 6
2.1.2 應力應變與應變能函數關係 8
2.1.3 動能及耗損能量 9
2.1.4 系統統御方程組 10
2.2 多孔材料參數介紹 14
2.2.1 孔洞係數 16
2.2.2 流體有效密度 16
2.2.3 流體體積模數 20
2.2.4 流阻係數 22
2.2.5 多孔材料參數與Biot 彈性係數之關係 25
第三章 多孔材料之拉普拉斯域有限元素分析理論 27
3.1 基本假設 27
3.2 二維有限元素 28
3.2.1 二維三角形有限元素 29
3.2.2 二維四邊形有限元素 32
3.3 三維四面體有限元素 35
3.4 邊界條件 41
第四章 有限元素分析與實驗結果比較 44
4.1 吸音係數量測 44
4.1.1 雙麥克風阻抗管實驗 45
4.1.2 量測設備 47
4.1.3 實驗步驟 48
4.2 有限元素分析與實驗結果比較 49
4.2.1 邊界限制於多孔吸音平板吸音係數之影響分析 51
4.2.2 角錐條型吸音板角錐外形變異對吸音係數之影響
60
4.2.2.1 對稱角錐條型吸音板 60
4.2.2.2 不對稱角錐條型吸音板 64
4.2.3 橢圓條型吸音板外形變異對吸音係數之影響 67
4.2.4 三維金字塔型吸音板外形變異對吸音係數之影響
71
第五章 結論與未來展望 76
5.1 結論 76
5.2 未來展望 77
參考文獻 79
符號對照表 83
圖目錄
圖2-1 ：泡棉吸音材料組織圖 16
圖2-2 ：圓管內流體速度分佈圖 17
圖2-3 ：泡棉吸音材料孔洞示意圖 23
圖3-1 ：三角形元素 30
圖3-2 ：三角形元素自然座標系示意圖 30
圖3-3 ：四邊形元素 32
圖3-4 ：四邊形元素自然座標系示意圖 33
圖3-5 ：四面體元素 37
圖3-6 ：四面體元素自然座標系示意圖 38
圖3-7 ：二維有限元素模型邊界限制示意圖 42
圖3-8 ：三維有限元素模型邊界限制示意圖 43
圖4-1 ：阻抗管與吸音材料示意圖 45
圖4-2 ：阻抗管實驗設備示意圖 48
圖4-3 ：三維圓柱體之四面體元素網格示意圖 50
圖4-4 ：三維矩形體之四面體元素網格示意圖 50
圖4-5 ：二維三角形元素網格示意圖 50
圖4-6 ：一維多孔平板示意圖 50
圖4-7 ：滾動邊界限制於一維、二維與三維分析影響比較
(0.0508m) 52
圖4-8 ：滾動邊界限制於一維、二維與三維分析影響比較
(0.040m) 53
圖4-9 ：滾動邊界限制於一維、二維與三維分析影響比較
(0.03m) 53
圖4-10：滾動邊界限制於一維、二維與三維分析影響比較
(0.016m) 54
圖4-11：固定邊界限制於一維、二維與三維分析影響比較
(0.0508m) 55
圖4-12：固定邊界限制於一維、二維與三維分析影響比較
(0.04m) 55
圖4-13：固定邊界限制於一維、二維與三維分析影響比較
(0.03m) 56
圖4-14：固定邊界限制於一維、二維與三維分析影響比較
(0.016m) 56
圖4-15：吸音係數量測與有限元素分析結果比較(0.0508m) 58
圖4-16：吸音係數量測與有限元素分析結果比較(0.04m) 58
圖4-17：吸音係數量測與有限元素分析結果比較(0.03m) 59
圖4-18：吸音係數量測與有限元素分析結果比較(0.016m) 59
圖4-19：對稱角錐條型幾何外形示圖 60
圖4-20：對稱角錐條型模型網格示意圖 61
圖4-21：各型對稱角錐條型吸音板吸音係數之頻域平均值比較 62
圖4-22：各對稱型角錐吸音係數之比較(I) 63
圖4-23：各對稱型角錐吸音係數之比較(II) 64
圖4-24：不對稱角錐條型幾何外形示意圖 65
圖4-25：不對稱條型角錐模型網格示意圖 65
圖4-26：各型不對稱角錐條型吸音板吸音係數之頻域平均值比較 66
圖4-27：各不對稱型角錐吸音係數之比較 67
圖4-28：橢圓條型吸音板幾何外形示意圖 68
圖4-29：橢圓條型吸音板模型網格示意圖 69
圖4-30：各型橢圓條型吸音板吸音係數之頻域平均值比較 69
圖4-31：各橢圓條型吸音板吸音係數之比較(I) 70
圖4-32：各橢圓條型吸音板吸音係數之比較(II) 71
圖4-33：金字塔型吸音板幾何外形示意圖 72
圖4-34：金字塔型吸音板模型網格示意圖 73
圖4-35：金字塔型吸音板吸音係數頻域平均值之比較 74
圖4-36：不同金字塔型吸音板吸音係數之比較(I) 75
圖4-37：不同金字塔型吸音板吸音係數之比較(II) 75
表目錄
表4.1：多孔材料參數 51
表4.2：材料厚度與剪力模數關係 51
表4.3：對稱角錐條型幾何外形尺寸表 61
表4.4：不對稱角錐條型幾何外型尺寸表 65
表4.5：橢圓條型幾何外形尺寸表 68
表4.6：金字塔型吸音板外形尺寸規格表 72

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