沉浸於不同液體中的梁之撓曲振動共振頻率

Abstract

本文以不同梁理論，推導沉浸液體中的梁之撓曲振動自然振模表示式與自然振頻。進而探討改變結構長厚比參數、無因次的材料常數比，從不同梁理論所得到的之間差異。以及沉浸不同液體環境下，從低自然振模到高自然振模，剪切梁理論和古典梁理論之間的自然振頻差異。最後引入有限元素軟體計算梁沉浸液體內的自然振動頻率，並探討模擬方法與各種梁理論之間差異。 在結果呈現長厚比、材料常數比和模態數是主要影響剪切梁理論和古典梁理論沉浸在液體中自然振動頻率比的之間差異性的關鍵因子。在液體環境對梁理論的影響程度發現與材料常數比率有很大的因數，越低材料常數比時液體的黏滯性影響成分大；在越高材料常數比時液體的密度影響成分大。其中在材料常數比為0.1的時候，此時液體的密度與黏滯性影響性皆最小的時候，所以頻率比的差異影響這時候僅只有長厚比與模態高低所影響著。最後在電腦模擬上，顯示三維模型上梁側面的水力負載間接影響梁的自然振頻。

This thesis studies the natural frequencies and mode shapes of flexural vibraion of beams immersed in fluids using different beam theories. Next, this work is devoted to investigating the effects of aspect ratio and material coefficient ratio(G/E) on the differences of resonant frequencies obtained from different models based on Euler-Bernoulli, Timoshenko, and Reddy beam theory. In addition, there is a discussion on the resonant frequency differences between shear beam theory and classical beam, which are immersed in air, water, and glycerin. Finally, the simulated results obtained by FEM software have been compared with the results of previous studies. The results of this thesis conclude that aspect ratio, material coefficient ratio ,and mode numder are the essential factors of the differences between shear beam theory and classical beam theory. Specially, the ratio G/E ratio has the great effect on the influence of by fluids. The viscosity of fluids plays an important role on the influence of natural frequencies predicted by different beam theories when the G/E ratio of beams is small, whereas the difference of natural frequencies obtained by different beam theories is influenced by the density of fluids mainly as the G/E ratio becomes large. Besides, the result points out that the natural frequency of Timoshenko beam theory would be same as one of Reddy beam theory even if the fluids are different while the G/E ratio of beams is equal to 0.1. Finally, the fact that the hydrodynamic loading due to viscosity acting on sides of thick beam affects the natural frequencies of beams has been observed from the FEM simulations.