耦合有限元素法與邊界積分式於隔音牆效能之分析

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林雍健(Yuo-Jian Lin ) 查詢紙本館藏

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機械工程研究所

論文名稱

耦合有限元素法與邊界積分式於隔音牆效能之分析

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摘要(中)

本文之目的在探討無限長度隔音牆之散射聲場，以往的研究大部分是使用邊界元素法來分析，
而本論文提出耦合有限元素法與邊界積分方程應用於隔音牆之散射聲場問題上，
文中並使用二維的形式來分析。本文所使用的方法避開了傳統邊界積分方程之奇異積分，
使得程式的設計既簡單又直接，同時也解決了有限元素法在處理外部聲場問題上的困難。
由測試結果顯示，所得到的數值解與解析解相比極為準確，
證實此方法應用在聲學問題上，為一有效且可靠的數值方法。
文中將對高度、形狀等隔音性能之影響因素進行探討，數值分析結果顯示，
高度為影響隔音牆性能之主要因素。此外，對於形狀之分析則顯示，
在T字形隔音牆上方加裝圓柱，則可以明顯提高隔音牆之性能。

摘要(英)

The purpose of this study is to analyze the scattering sound field of a infinite length barrier.
Most of the researches regarded barrier anaiysis as a boundary element method.
This study presents the application of the coupled Finite Element Method and Boundary Integral Equation for the
scattering by rigid barrier in a sound field. The two dimensional consideration is adopted in present work.
The coupled method avoids the well-known singularity of Boundary Integral Equation
and eliminates the difficulties when the FEM handles the exterior acoustics.
The implementation is a straight forward and easy process.
The numerical results are very accurate compared to analytical solutions.
It is proved that this method is an efficient and reliable numerical method in handling the acoustic problems.
The acoustic performance infinence factors, such as height and shape of a barrier are also investigated.
From numerical results, one can find that height is the most important factor on barrier performance.
Further, barrier shape can also affect the performance effectively. A rectangular barrier with cylindrical
top can strongly raise the overall performance of a barrier choice in barrier design.

關鍵字(中)

★ 二維
★ 插入損失
★ 放射
★ 散射
★ 有限元素法
★ 邊界元素法
★ 隔音牆

關鍵字(英)

★ barrier
★ boundary element method
★ finite element method
★ insertion loss
★ radition
★ scattering
★ two -dimensional

論文目次

中文摘要 I
英文摘要 II
誌謝 III
目錄 IV
圖目錄 VI
表目錄 VIII
符號說明 IX
第一章緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 本文架構 4
第二章有限元素公式 6
2.1 二維聲場有限元素公式推導 6
2.2 數值解法 9
第三章邊界元素公式 13
3.1 二維聲場邊界積分公式推導 13
3.2 非唯一性問題 17
3.3 數值解法 21
第四章耦合有限元素法與邊界積分式 23
4.1 耦合的基本原理 23
4.2 耦合公式推導 24
4.3 非唯一性問題 26
4.4 半平面問題公式推導 27
4.5 散射問題公式推導 30
第五章實例測試與討論 32
5.1 程式測試 32
5.2 隔音牆分析 39
5.2.1 高度的影響 41
5.2.2 形狀的影響 48
第六章結論 54
參考文獻 56
附錄A 求解Bessel function的程式 61
附錄B 求解Bessel function的程式 63

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指導教授

鄔蜀威(Shu-Wei Wu)

審核日期

2001-6-21

推文