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系統識別號 U0002-0308201601240300
中文論文名稱 應用序列二次規劃於上表面半橢圓形條型泡棉最佳化設計
英文論文名稱 Application of Sequential Quadratic Programming to the Optimal Design of Corrugated Foam with Semi-Elliptical Strip Profile
校院名稱 淡江大學
系所名稱(中) 機械與機電工程學系碩士班
系所名稱(英) Department of Mechanical and Electro-Mechanical Engineering
學年度 104
學期 2
出版年 105
研究生中文姓名 許文才
研究生英文姓名 Wen-Tsai Shiu
學號 603350041
學位類別 碩士
語文別 中文
口試日期 2016-06-03
論文頁數 65頁
口試委員 指導教授-葉豐輝
委員-葉豐輝
委員-蔡慧駿
委員-柯德祥
中文關鍵字 Biot多孔彈性理論  有限元素頻域分析  脈衝響應  吸音係數  序列二次規劃 
英文關鍵字 Biot’s Poroelastic Theory  Finite Element Frequency Domain Analysis  Impulse Response  Sound Absorption Coefficient  Sequential Quadratic Programming 
學科別分類 學科別應用科學機械工程
中文摘要 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。
英文摘要 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.
論文目次 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

參考文獻 1. M. A. Biot, “General Theory of Three-Dimensional Consolidation”, Journal of Applied Physics, Vol. 12, No. 2, pp. 155-164, 1941.
2. M. A. Biot, “Theory of Elasticity and Consolidation for a Porous Anisotropic Solid”, Journal of Applied Physics, Vol. 26, No. 2, pp. 182-185, 1955.
3. M. A. Biot, “Theory of Propagation of Elastic Waves in A Fluid‐Saturated Porous Solid. I. Low‐Frequency Range”, the Journal of the Acoustical Society of America, Vol. 28, No. 2, pp. 168-178, 1956.
4. M. A. Biot, “Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range”, The Journal of the Acoustical Society of America, Vol. 28, No. 2, pp. 179-191, 1956.
5. M. E. Delany and E. N. Bazley, “Acoustical Properties of Fibrous Absorbent Materials”. Applied Acoustics, Vol. 3, No. 2, pp. 105-116, 1970.
6. J. F. Allard, C. Depollier and A. L’Esperance, “Observation of the Biot Slow Wave in a Plastic Foam of High Flow Resistance at Acoustical Frequencies”, Journal of Applied Physics, Vol. 59, No. 10, pp. 3367-3370, 1986.
7. Y. Miki, “Acoustical Properties of Porous Materials-Modifications of Delany-Bazley Models”, Journal of the Acoustical Society of Japan, Vol. 11, No. 1, pp. 19-24, 1990.
8. M. R. Stinson, “The Propagation of Plane Sound Waves in Narrow and Wide Circular Tubes, and Generalization to Uniform Tubes of Arbitrary Cross‐Sectional Shape”, The Journal of the Acoustical Society of America, Vol. 89, No. 2, pp. 550-558, 1991.
9. 黃忠良,“多孔材料學”,復漢出版社,1990。
10. F.-H. Yeh and H.-S. Tsay, “Dynamic Behavior of a Poroelastic Slab Subjected to Uniformly Distributed Impulsive Loading”, Computers and Structures, Vol. 67, No. 4, pp. 267-277, 1998.
11. 蔡慧駿、葉豐輝,“有限長度多孔性吸音平板之動態音響阻抗分析與量測”,行政院國家科學委員會專題研究計畫成果報告,計畫編號:NSC86-2212-E-032-005,pp. 1-107,1997。
12. 王新榮,“有限元素法及其應用”,中央圖書出版社,1997。
13. 黃耀漢,“多孔材料與吸振與吸音之應用”,碩士論文,淡江大學機械與機電工程學系,1999。
14. W.-H. Chen, F.-C. Lee and D.-M. Chiang, “On the Acoustic Absorption of Porous Materials with Different Surface Shapes and Perforated Plates”, Journal of Sound and Vibration, Vol. 237, No. 2, pp. 337-355, 2000.
15. N. Atalla, R. Panneton, F. C. Sgard and X. Olny, “Acoustic Absorption of Macro-Perforated Porous Materials”. Journal of Sound and Vibration, Vol. 243, No. 4, pp. 659-678, 2001.
16. M. Schanz, “Application of 3D Time Domain Boundary Element Formulation to Wave Propagation in Poroelastic Solids”, Engineering Analysis with Boundary Elements, Vol. 25, No. 4, pp. 363-376, 2001.
17. 蔡慧駿、葉豐輝、丁國書,纖維吸音複合板吸音係數設計-複數動態勁度法,中國機械工程學會第十八屆全國學術研討會,pp. 399-406,2001。
18. 丁國書,“角錐與金字塔吸音板之吸音係數設計”,碩士論文,淡江大學機械與機電工程學系,2002。
19. 張政斌,“邊界限制於多孔材料吸音係數之影響分析”,碩士論文,淡江大學機械與機電工程學系,2002。
20. H.-S. Tsay and F.-H. Yeh, “Frequency Response Function for Prediction of Planar Cellular Plastic Foam Acoustic Behavior”, Journal of Cellular Plastics, Vol. 41, pp. 101-131, 2005.
21. H.-S. Tsay and F.-H. Yeh, “Finite Element Frequency-Domain Acoustic Analysis of Open-Cell Plastic Foams”, Finite Element in Analysis and Design, Vol. 42, pp. 314-339, 2006.
22. H.-S. Tsay and F.-H. Yeh, “Optimal Design of Corrugated Cellular Plastic Foam with Semi-Elliptical Shaped Upper Surface by Finite Element Frequency Domain Acoustic Analysis”, Journal of Cellular Plastics, Vol. 43, pp. 197-214, 2007.
23. D. Soares and W. J. Mansur, “A Time Domain FEM Approach Based on Implicit Green's Functions for Dynamic Analysis of Porous Media”, Computer methods in applied mechanics and engineering, Vol. 197, pp. 4645-4652, 2008.
24. H.-S. Tsay and F.-H. Yeh, “Analysis of Mode Shapes of a Rigidly Backed Cylindrical Foam”, Applied Acoustics, Vol. 69, No. 9, pp. 778-788, 2008.
25. 吳鑄成,“加肋多孔板與聲場耦合之脈衝響應”,碩士論文,淡江大學機械與機電工程學系,2012。
26. 白明憲,“工程聲學”,全華科技圖書公司,台北市,2014。
27. W. Chen, S. Liu, L. Tong and S. Li, “Design of Multi-Layered Porous Fibrous Metals for Optimal Sound Absorption in the Low Frequency Range”, Theoretical and Applied Mechanics Letters, 2016
28. D. Lafarge, P. Lemarinier, J. F. Allard and V. Tarnow, “Dynamic Compressibility of Air in Porous Structures at Audible Frequencies”, The Journal of the Acoustical Society of America, Vol. 102, No. 4, pp .1995-2006, 1997.
29. M. Henry, P. Lemarinier, J. F. Allard, J. L. Bonardet and A. Gedeon, “Evaluation of the Characteristic Dimensions for Porous Sound‐Absorbing Materials”, Journal of Applied Physics, Vol. 77, No. 1, pp. 17-20, 1995.
30. B. S. Kim, S. J. Cho, D. K. Min and J. Park, “Experimental Study for Improving Sound Absorption of Composite Helical-Shaped Porous Structure Using Carbon Fiber”, Composite Structures, Vol. 145, pp. 242-247, 2016.
31. X. L. Gai, X. H. Li, T. Xing, B. Zhang and J. J. Zhao, “Experimental Study on Sound Absorption Performance of Microperforated Panel with Membrane Cell”, Institute of Noise Control Engineering, Vol. 250, No. 6, pp. 1032-1039, 2015.
32. J. Nocedal and S. Wright, “Numerical optimization”, Springer Science and Business Media, 2006.
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