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研究生:彭子桓
研究生(外文):Tzu-Huan Peng
論文名稱:填充無黏性液體之彈性圓管聲傳研究
論文名稱(外文):Acoustic Wave Propagation in a Cylindrical Elastic Tube Filled with Inviscid Liquid
指導教授:周元昉
指導教授(外文):Yuan-Fang Chou
口試委員:盧中仁莊嘉揚
口試委員(外文):Chung-Jen LuJia-Yang Juang
口試日期:2014-07-28
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:中文
論文頁數:100
中文關鍵詞:填充無黏性液體之彈性圓管波導頻散曲線
外文關鍵詞:Cylindrical Elastic Tube Filled with Inviscid LiquidWaveguidedispersion curve
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為探究耳蝸力學,本文研究「填充無黏性液體之彈性圓管」模型之聲傳,以解釋耳蝸內聲傳之特殊現象-快波與慢波、速度極慢的行波。
在彈性圓管內含無黏性液體模型之聲傳研究,分別建立彈性管與液體的統御方程式,然後加入合適邊界條件與材料參數,以數值軟體計算,得到該模型之波傳頻散曲線及各模態之位移振形。
觀察其頻散特性,發現其第1模態與第2模態之頻散曲線無截止頻率,且由振形可知分別源自液體以及彈性管的平面波傳,由相速圖亦發現此兩個模態速度極慢,以上模態特徵解釋耳蝸內聲傳之特殊現象。
另外發現在高頻處會出現液體模態顯著的區域;模態在大部分區域都是彈性管的位移振形較顯著,但到了液體影響顯著的區域時,則轉由液體振形較顯著,且群速變極快。


In this article, the acoustic wave propagation in the model “Cylindrical Elastic Tube Filled with Inviscid Liquid” is studied, for explaining special acoustic propagation phenomena in the cochlear - fast wave and slow wave, and traveling wave with well slow velocity.
In the study of the model “Cylindrical Elastic Tube Filled with Inviscid Liquid”, the governing equations of tube and liquid with appropriate material parameters and boundary conditions, are solved by MATLAB to get the dispersion curve and the mode shapes.
Investigation the dispersion curve and mode shapes of the model, it can be found that there’s no cutoff frequency in the 1st and 2nd mode, which originate from the plane wave of liquid and tube, and they also have well slow velocity just as the phase velocity plot showing. The characteristic in the model above can explain the wave propagation phenomena in the cochlear.
Besides, it is found the modes of liquid appear significantly in the high frequency place. In these areas, the mode shape of the liquid part is larger and the group velocity is faster than those in the other areas.


摘要……………………………………………i
Abstract………………………………………ii
目錄………………………………………………iii
表目錄…………………………………………v
圖目錄…………………………………………vi
符號表……………………………………………viii
第一章 緒論………………………………- 1 -
1.1 前言 - 1 -
1.2 研究動機 - 1 -
1.3 文獻回顧 - 2 -
1.3.1 彈性管內含液體之波傳 - 2 -
1.3.2 耳蝸力學 - 3 -
1.4 章節內容 - 4 -
第二章 耳蝸之結構與數學模型……….. - 5 -
2.1 耳蝸基本結構 - 5 -
2.2 耳蝸的聲波傳遞 - 5 -
2.3 本文採用之模型 - 6 -
第三章 彈性圓管內含無黏性液體之波傳統御方程式 - 8 -
3.1 彈性管 - 8 -
3.1.1 彈性管的統御方程式 - 8 -
3.1.2 彈性管的位移和應力 - 9 -
3.2 管內液體 - 13 -
3.2.1 尤拉方程式 - 13 -
3.2.2 連續方程式 - 14 -
3.2.3 狀態方程式 - 14 -
3.2.4 液體的統御方程式 - 15 -
3.2.5 液體的位移、應力和壓力 - 15 -
3.3 邊界條件 - 17 -
3.4 求解 - 18 -
第四章 結果與討論……………………………… - 21 -
4.1 第1模態與第2模態 - 22 -
4.2 L線 - 23 -
4.3 液體與彈性管的交互影響 - 24 -
4.4 「彈性軟管含液體」模型與耳蝸波傳現象 - 26 -
第五章 結論與建議………………… - 27 -
附錄A 輸入阻抗……………………… - 29 -
附錄B 彈性管內含無黏性液體位移解的正交性 - 31 -
參考文獻…………………………………………… - 38 -
附表…………………………………………… - 41 -
附圖…………………………………………… - 45 -


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