# 臺灣博碩士論文加值系統

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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 IIIAbstract IV1緒論 11.1前言 11.2文獻回顧 31.2.1流體理論 31.2.2梁理論 41.2.3流固耦合及實驗 41.3論文架構 62理論介紹 72.1水力函數 92.2 古典梁理論 112.3 一階剪切變形梁理論 142.4 三階剪切變形梁理論 193計算方法與驗證 273.1計算方法 273.2與文獻驗證 293.2.1懸臂梁感測器 293.2.2 橋式感測器 324 數值結果 354.1 懸臂梁感測器 364.1.1 長厚比的影響 364.1.2 材料性質的影響 464.1.3流體的影響 544.2 橋式感測器 614.2.1 長厚比的影響 614.2.2 材料性質的影響 654.2.3 流體的影響 725 結論及未來展望 845.1結論 845.1.1 微懸臂梁 845.1.2 橋式梁 865.2未來展望 87參考文獻 88附錄 91A三階剪切變形梁各式邊界 91B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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