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

Application of Sequential Quadratic Programming to the Optimal Design of Corrugated Foam with Semi-Elliptical Strip Profile

許文才(Wen-Tsai Shiu)

指導教授 ： 葉豐輝

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2016年)

https://doi.org/10.6846/TKU.2016.00097

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。

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

並列摘要

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.

並列關鍵字

Biot’s Poroelastic Theory ； Finite Element Frequency Domain Analysis ； Impulse Response ； Sound Absorption Coefficient ； Sequential Quadratic Programming

參考文獻

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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.

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