本文旨在探討含飽和流體條型泡棉之上表面半橢圓形吸音係數最佳化設計。本研究使用Biot多孔彈性理論於頻域中並應用Galerkin型態有限元素法推導二維四邊形元素之剛性矩陣及荷重向量，給予材料參數及邊界條件，直接求得泡棉上表面流體與固體之平均位移，並計算求其動態複數勁度(CDS)與吸音係數(SAC)。
本研究首先驗證分析方法之正確性，分析所得之上表面橢圓邊界動態複數勁度及其吸音係數與前人所發表結果一致，顯示本文有限元素頻域分析(FEFDA)可精確模擬多孔材料吸音係數。其次應用序列二次規劃(SQP)進行條型泡棉上表面半橢圓形吸音係數最佳化分析，分別探討不同截面寬度比(MWR)於低頻(0~2000Hz)、中頻(1000~3000Hz)及高頻(2000~4000Hz)最佳吸音係數，經由分析結果顯示，泡棉在相同面積約束下之截面寬度比於低頻、中頻及高頻分別為MWR=0.33、MWR=0.34及MWR=1.31時可得到最佳吸音係數。

This thesis attempted to provide an optimal design of semi-elliptic sound absorption coefficient on the surface of corrugated foam mixed with saturated fluid. Biot’s poroelastic theory was integrated into the study of frequency domain, Galerkin type finite element approach was employed to derive the rigid matrix as well as the force vector of two-dimensional quadrilateral elements, and with the given material parameters and boundary conditions, the mean displacement of fluids and solids on the surface of foam were obtained. Based on the results stated above, the complex dynamic stiffness (CSD) and sound absorption coefficient (SAC) were obtained.
Firstly, analysis method was validated to make sure it was appropriate for this study. The results indicated that the complex dynamic stiffness and sound absorption coefficient on the surface of elliptic border were exactly the same as the results released by previous researchers. Apparently, the finite element frequency domain analysis (FEFDA) employed by this study was sufficient to simulate porous materials’ sound absorption coefficient precisely. Secondly, sequential quadratic programming (SQP) was employed to analyze the optimization of semi-elliptic sound absorption coefficient on the surface of corrugated foam, attempting to find out the optimal sound absorption coefficient of different sectional width ratios (MWR) at low frequency (0~2000Hz), medium frequency (1000~3000Hz), and high frequency (2000~4000Hz), respectively. According to the analysis results, optimal sound absorption coefficient was gained when foam was restricted by same area in which MWR was 0.33, 0.34, and 1.31 at low frequency, medium frequency, and high frequency, respectively.

目  錄
中文摘要	I
英文摘要	II
目  錄	IV
圖目錄	VI
表目錄	VIII
係數定義對照表	IX
第一章 緒論	1
1.1 前言	1
1.2 研究動機	2
1.3 文獻回顧	4
1.4 研究內容	5
第二章 基本理論	7
2.1 多孔材料之統御方程組	7
2.1.1 應力、應變及位移關係	7
2.1.2 應力應變與應變能函數關係	9
2.1.3 動能及消散能量	10
2.1.4 統御方程組	11
2.1.5表面可穿透式吸音係數理論	15
2.1.6表面不可穿透式吸音係數理論	18
2.2 多孔材料參數	20
2.2.1 孔洞係數	21
2.2.2 材料密度	22
2.2.3 結構因子	22
2.2.4 空氣體積模數	23
2.3 材料係數與Biot彈性係數之關聯性	23
2.4 最佳化設計理論	24
2.4.1 序列二次規劃演算理論	26
第三章 有限元素頻域分析	29
3.1 基本假設	29
3.2 多孔彈性介質二維動態統御方程推導	30
3.2.1 多孔介質二維四邊形元素	32
3.2.2 邊界條件	36
第四章 結果與討論	38
4.1 聲響阻抗	38
4.2 吸音係數	39
4.3 降噪係數	40
4.4上半橢圓形條型泡棉之三角形與四邊形元素誤差比較	40
4.5 序列二次規劃最佳化分析結果	48
4.5.1 低頻吸音係數之半主軸長分析(0000~2000 Hz)	49
4.5.2 中頻吸音係數之半主軸長分析(1000~3000 Hz)	52
4.5.3 高頻吸音係數之半主軸長分析(2000~4000 Hz)	54
4.6 含飽和流體之吸音泡棉表面平均位移時域分析	57
第五章 結論與未來展望	59
5.1 結論	59
5.2 未來展望	60
參考文獻	62 
圖目錄
圖2-1	音波射穿至可穿透表面之多孔材料示意圖	16
圖2-2	音波射穿至不可穿透表面之多孔材料示意圖	18
圖2-3	SQP循環迭代過程示意圖	28
圖3-1	多孔介質二維任意四邊形元素直角座標系示意圖	32
圖3-2	多孔介質四邊形元素自然座標系示意圖	33
圖3-3	二維邊界條件示意圖	37
圖4-1	聲波傳播路徑示意圖	39
圖4-2	上表面半橢圓形條型吸音泡棉	41
圖4-3	上半橢圓受一瞬間衝擊負荷示意圖	41
圖4-4	二維上半橢圓吸音泡棉之邊界條件	42
圖4-5	上表面半橢圓邊界複數動態勁度實部(三角形及四邊形元素)	46
圖4-6	上表面半橢圓邊界複數動態勁度虛部(三角形及四邊形元素)	46
圖4-7	三角形及四邊形元素之條形泡棉吸音係數分析	48
圖4-8	上半橢圓形材料示意圖	49
圖4-9	上半橢圓形條型泡棉之低頻平均吸音係數分析	51
圖4-10	上半橢圓形條型泡棉截面寬度比之低音吸音係數分析	51
圖4-11	上半橢圓形條型泡棉之中頻平均吸音係數分析	53
圖4-12	上半橢圓形條型泡棉截面寬度比之中音吸音係數分析	54
圖4-13	上半橢圓形條型泡棉之高頻平均吸音係數分析	56
圖4-14	上半橢圓形條型泡棉截面寬度比之高音吸音係數分析	57
圖4-15	低頻、中頻及高頻之頻率域轉時域平均位移分析	58

 
表目錄
表4-1	上半橢圓形條型幾何尺寸	42
表4-2	四邊形元素之網格節點元素表	43
表4-3	含飽和空氣與泡棉材料參數表	44
表4-4	低頻最佳化網格示意圖	50
表4-5	中頻最佳化網格示意圖	52
表4-6	高頻最佳化網格示意圖	55

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