臺灣博碩士論文加值系統

本文旨在進行一種三維時間域聲壓場邊界積分方程時間內插新解法之研究，過程是以三維時間域聲壓場邊界積分方程(BIE)與邊界元素法(BEM)進行時間域逐步計算聲壓分佈。
文中為求所撰寫程式之正確性，將先以密閉三維立體剛性邊界聲場之映像法解析比較做驗證，接著是以邊界積分方程計算直接音與一次反射音，積分方程計算過程以邊界元素法計算一次以上反射音之混響，即可得到室內聲場聲壓的歷時序列。由於聲壓場為動態，不論時空皆劇烈振盪，本文邊界元素法中的幾何與物理特性採用三角形線性面元素(T3)與四邊形元素(Q8)兩種函數，時間域則以傅立業(Fourier)級數展開進行時間內插，並輔以線性時間內插作比對，以改善時間域不易收斂的問題。

The aim of this dissertation is to develop a time domain acoustic computation theory, which is calculating the sound pressure distribution of three dimensional enclosure for boundary integral equation with a new time interval algorithm.
In order to ensure the accuracy of the boundary integral program compared with the image method for a three dimensional enclosed source field. Based on the equation developed are a calculation procedure BIE for the direct sound and the first reflected sound, and a time domain boundary element method (BEM) for calculating the subsequent part of the sound pressure. The sound pressure, which exhibits notoriously large oscillations in bath space and time domains, it is proposed that interpolations are always carried out on boundary pressure with triangular element and quadrangle element in geometric and physical properties. The time domain interpolations are carried out with Fourier series expansion function compared with linear. The convergence problems can be improved based on the above calculation in the BIE and BEM procedures.

第一章 導論 1
1.1 研究背景與動機 1
1.2 文獻回顧 2
1.3 本文介紹與架構 3
第二章 室內三維聲場時間域邊界積分方程 5
2.1 三維聲場時間域聲波傳播邊界積分方程 5
2.2 脈衝響應函數的模擬 8
2.3 脈衝響應函數之邊界積分方程 10
第三章 分析方法 12
3.1 具體求法概論 12
3.2 一次反射音在邊界的影響區域 12
3.3 直接音及一次反射音 27
3.3.1 一次反射的邊界積分方程 27
3.4 一次以上反射音 30
3.4.1 空間內插函數 30
3.4.2 時間內插函數 31
3.4.3 邊界元素離散化推導 34


第四章 長方體數值計算 36
4.1 映像法解析解 36
4.1.1音源時間項以單頻表示 36
4.1.2音源時間項以頻帶表示 37
4.2 以諧波穩定聲場對傅立葉項數改變之分析 37
4.3 邊界積分與邊界元素法計算 38
4.3.1音源時間項以諧波表示 38
4.3.2音源時間項以頻帶表示 39
4.3.3邊界積分方程計算流程 39
4.4 數值計算結果 41
4.4.1原尺寸空間與縮小尺寸0.4的影響 41
4.4.2映像法與邊界元素法之聲壓大小比較 42
4.4.3映像法與邊界元素法之聲壓實部與虛部 44
4.4.4傅立葉級數改變N之影響 44
第五章 結果與討論 46
參考文獻 47
附錄A 映像法 85

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