本論文檢視以音效合成方法中的物理模擬法( physical modeling synthesis )對多種樂器結構進行模擬的成果。物理模擬法將製造聲音的物理機制考慮進去，可藉以瞭解樂器震動的情形與其發聲的物理現象，能得到最佳的音效品質。本論文針對下列三種結構進行模擬：
(1) 薄膜：直接解描述此問題的數學方程式。
(2) 矩形平板：除了直接解描述此問題的數學方程式以外，對於沒有精確解的邊界情形，我們利用有限元素法( finite element method ) 來求其近似解。
(3) 吉他樂器：以一個包含弦和共振箱的簡單物理模型，分別將弦與共振箱的模擬組合起來。
模擬所得的聲響與我們的實際體驗相符。

The subject of this thesis is in examining simulated results of the physical modeling of several structures of musical instruments. Physical modeling is one of the promising methods of sound synthesis. By modeling the mechanism of sound production, physical model synthesis provides not only the relationship between the vibration and acoustic phenomena of musical instruments, but also the digital sound with the best auditory quality. Three kinds of musical instruments are simulated in this thesis:
(1) membranes : The equations of this problem are solved directly.
(2) rectangular plates : For plate problems that do not have exact solutions, we utilize the finite element method to obtain those approximate solutions.
(3) guitar : Based on a simple physical model of strings and a soundboard, we are able to simulate the sound of a guitar.
Simulated sounds are consistent with our listening experiences.

第一章 緒論
1.1 引言
1.2 研究背景與動機
1.3 章節介紹
第二章二維系統振動模擬(一) 薄膜
2.1 矩形薄膜之波方程式
2.2 矩形薄膜振動之遠場聲響
第三章二維系統振動模擬(二) 有限元素法與矩形平板
3.1 矩形平板問題簡介
3.2 變分法求解
3.3 有限元素法的求解過程
3.3.1 值域分割
3.3.2 元素的內插
3.3.3 由Ritz法求解
3.4 模擬結果
第四章三維系統振動模擬吉他樂器
4.1 吉他樂器的物理模型
4.2 吉他共振箱之振動模態
4.3 吉他共振箱之暫態響應
4.4 吉他發聲模擬
第五章 結論
參考資料
附錄：聲音音效實例

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