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研究生:
研究生(外文):Muh-Jang Chen
論文名稱:沉浸在不同流體之剪切變形梁共振頻率的一階及三階理論研究
論文名稱(外文):Study of resonant frequencies of the first and third order shear deformation beam theories immersed in fluids
指導教授:張正憲張正憲引用關係
指導教授(外文):Jeng-Shian Chang
口試委員:吳光鐘陳世豪
口試委員(外文):Kuang-Chong Wu
口試日期:2015-07-23
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:應用力學研究所
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:2015
畢業學年度:103
語文別:中文
論文頁數:93
中文關鍵詞:一階剪切變形理論梁理論三階剪切變形理論梁理論微懸臂梁橋式梁共振頻
外文關鍵詞:Timoshenko beam theoryReddy beam theorymicro-cantilevermicro-bridgeresonant frequency
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本文致力於應用不同梁理論建立懸臂梁和橋式梁沉浸於流體中振動的模型,佐以文獻實驗數據,加以比對驗證。首先以古典梁搭配Sader之水力函數建立基礎模型。接著應用一階及三階剪切變形理論搭配相同之水力函數建立模型。應用兩種梁的邊界之後,以掃頻的方式找出剪切變形理論之共振頻。最後長厚比和材料參數對剪切變形理論和古典梁理論之差異造成的影響,並探討在長厚比和材料參數下,三種環境對三種梁理論之共振頻差異的影響。

This thesis studies the resonant frequencies of cantilevered and fixed-fixed (bridge) beams immersed in fluids using 1st order and 3rd order shear-deformable beam theories. First, the classic model is developed under Euler-Bernoulli beam theory (EBT) and the hydrodynamic function presented by Sader. Second, the Timoshenko beam theory (TBT) which is a first order shear deformation beam theory and the Reddy beam theory (RBT) which is a third order one are applied to develop new models for biosensors. To obtain the resonant frequencies, boundary conditions of cantilever and bridge beams are both presented. Third, the theoretical prediction developed in this thesis is compared with the experimental data in the literature. Forth, this work is devoted to investigating the effects of aspect ratio and material coefficient ratio on the differences of resonant frequencies obtained from different models. Finally, to investigate the influences in fluids with different viscosities, water and glycerin are considered.

口試委員會審定書 I
致謝 II
摘要 III
Abstract IV
1緒論 1
1.1前言 1
1.2文獻回顧 3
1.2.1流體理論 3
1.2.2梁理論 4
1.2.3流固耦合及實驗 4
1.3論文架構 6
2理論介紹 7
2.1水力函數 9
2.2 古典梁理論 11
2.3 一階剪切變形梁理論 14
2.4 三階剪切變形梁理論 19
3計算方法與驗證 27
3.1計算方法 27
3.2與文獻驗證 29
3.2.1懸臂梁感測器 29
3.2.2 橋式感測器 32
4 數值結果 35
4.1 懸臂梁感測器 36
4.1.1 長厚比的影響 36
4.1.2 材料性質的影響 46
4.1.3流體的影響 54
4.2 橋式感測器 61
4.2.1 長厚比的影響 61
4.2.2 材料性質的影響 65
4.2.3 流體的影響 72
5 結論及未來展望 84
5.1結論 84
5.1.1 微懸臂梁 84
5.1.2 橋式梁 86
5.2未來展望 87
參考文獻 88
附錄 91
A三階剪切變形梁各式邊界 91
B不同梁之三階剪切變形梁理論行列式 92
懸臂梁 92
簡支梁 93


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