黏滯流體下一階及三階梁理論側向振動之模態頻率研究

Abstract

本文分別引用一階剪切變形梁理論、三階剪切變形梁理論及古典梁理論描述梁結構之振動行為，並結合水力函數將流體之影響引入梁的模態分析，藉由改變梁結構的長厚比、材料常數(G/E ratio)比及流體環境，探討其對梁模態頻率預測之影響。 結果顯示，長厚比、材料常數比及模態數的大小為影響各種梁理論之間差異性的主要因子。而流體環境對預測頻率之差異性影響主要來自於流體的密度及黏滯力，在低材料常數比時，受流體的影響主要來自於黏滯力；而高材料常數比時則由流體密度影響較甚；當材料常數比介於0.1到0.05之間時，結構受到流體之影響為最小。

In this paper, we present the natural frequencies and mode shapes of the flexural vibration of different beam theories, Euler-Bernoulli beam theory (EBT) , Timoshenko beam theory (TBT) and Reddy beam theory (RBT), immersed in the viscous fluid. Furthermore, we research in different effects of natural frequencies between not only EBT and TBT but EBT and RBT due to different aspect ratio and dimensionless material properties, the G/E ratio. From the results, we conclude that aspect ratio, dimensionless material properties, and mode number play important roles in different beam models immersed in the viscous fluid. The dominant factor of beam structure immersed in the fluid with low G/ E ratio is fluid viscosity, whereas the fluid density with high G/E ratio. However, the result points out when the G/E ratio from 0.05 to 0.1, the influence of fluid viscosity and density will reduce to vanish. Accordingly, we should only consider the effect of aspect ratio and mode number.