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

Study of resonant frequencies of the first and third order shear deformation beam theories immersed in fluids

10.6342/NTU.2015.02916

陳⿬璋

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 ； Timoshenko beam theory ； Reddy beam theory ； micro-cantilever ； micro-bridge ； resonant frequency

臺灣大學應用力學研究所學位論文

2015年

碩士

張正憲

繁體中文

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.

1. 戴源志(2016)。沉浸於不同液體中的梁之撓曲振動共振頻率。臺灣大學應用力學研究所學位論文。2016。1-171。