沉浸於不同液體中的梁之撓曲振動共振頻率

戴源志

doi:10.6342/NTU201602270

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沉浸於不同液体中的梁之挠曲振动共振频率

Study of resonant frequencies of flexural vibration of beams immersed in various fluids

戴源志 , 硕士　　导师：张正宪　　

繁体中文 DOI： 10.6342/NTU201602270

一阶剪切梁理论；三阶剪切梁理论；动态梁表示式；电脑模拟； Timoshenko beam theory ； Reddy beam theory ； dynamic vibration of beam ； computed simulation

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摘要 │ 参考文献 (34) │ 国际计量

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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.

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[2] D. A. Walters, J. P. Cleveland, N. H. Thomson, P. K. Hansma, M. A. Wendman, G. Gurley, &V. Elings. (1996). "Short cantilevers for atomic force microscopy," Review of Scientific Instruments, 67(10), pp. 3583-3590.
连结：
[5] T. Thundat, E. A. Wachter, S. L. Sharp, &R. J. Warmack. (1995). "Detection of mercury vapor using resonating microcantilevers," Applied Physics Letters, 66(13), pp. 1695-1697.
连结：
[6] C. Ziegler. (2004). "Cantilever-based biosensors," Analytical and bioanalytical chemistry, 379(7-8), pp. 946-959.
连结：
[7] S. P. Timoshenko. (1921). "On the correction for shear of the differential equation for transverse vibrations of prismatic bars," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 41(245), pp. 744-746.
连结：
[9] M. Levinson. (1981). "A new rectangular beam theory," Journal of Sound and Vibration, 74(1), pp. 81-87.
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DOI可强化引用精确性、增强学术圈连结，并给予使用者跨平台的良好使用经验，目前在全世界已有超过五千万个对象申请DOI。如想对DOI的使用与概念有进一步了解，请参考（）。