奇異項重建法在二維聲場邊界元素分析之應用

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姓名

李訓良(Hsun-Liang Lee) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

奇異項重建法在二維聲場邊界元素分析之應用
(Singularity-Term Reconstruction for Boundary Element Analysis ofTwo-Dimensional Acoustic Problems)

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摘要(中)

在傳統的工程問題上，求解邊界積分式時，會遇到源點與場點重合所產生的奇異性問題，而在方程式係數矩陣的對角線項產生誤差。一般要解決這個問題都必須用到複雜的方程式及數學推導，使得程式設計的過程非常繁瑣。
本文提出奇異項重建法，在振動體內部任意取兩個簡單點聲源，以該聲源所產生的邊界上聲壓與速度的理論值，作為方程式的已知值，得到兩組聯立方程式，逆算產生方程式中對角線奇異項的係數，完成方程式的係數矩陣，用以計算所要分析的未知聲場。本文以二維聲波場的放射與散射為實例，邊界上使用三節點二次式等參元素，所得到的數值解與解析解相比較均極為準確，證實此方法用在聲學問題上，為一有效且可靠的數值方法。

摘要(英)

The purpose of this study is to handle the well-known singularity problems of Boundary Integral Equation. This study presents the application of singularity-term reconstruction method. By using known vibrating boundary conditions, which are gotten by setting two simple point sources in the vibration body, we get the singularity-terms without using complicated formulations. The two-dimensional acoustic radiation and scattering problems were tested. The three-noded curvilinear elements were adopted. 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.

關鍵字(中)

★ 邊界元素法
★ 奇異項重建法
★ 奇異性

關鍵字(英)

★ Singularity-Term Reconstruction Method
★ Boundary Element Method
★ Singularity

論文目次

目錄頁數
中文摘要..........................................I
英文摘要.........................................II
誌謝............................................III
目錄.............................................IV
圖表總覽.........................................VI
符號說明.......................................VIII
一、緒論..........................................1
1.1 研究動機.....................................1
1.2 文獻回顧.....................................2
1.3 本文架構.....................................4
二、二維聲場之邊界積分公式........................6
2.1 Helmholtz積分式..............................6
2.2 非唯一性問題.................................8
2.3 數值計算公式.................................9
2.4 數值演算....................................13
三、奇異項公式原理推導...........................16
四、實例測試與討論...............................20
4.1 圓形振動體的聲場放射........................20
4.2 特徵波數的非唯一性..........................23
4.3 長方形振動體的聲場放射......................24
五、聲波散射.....................................29
5.1 散射公式基本原理............................29
5.2 實例測試....................................31
六、結論.........................................36
參考文獻.........................................38
附錄A 求解Bessel function$J_0$、$Y_0$的程式......42
附錄B 求解Bessel function$J_1$、$Y_1$的程式......44

參考文獻

參考文獻
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指導教授

鄔蜀威(Shu-Wei Wu)

審核日期

2002-7-11

推文