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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 張正憲 | |
dc.contributor.author | Rui-Yi Wang | en |
dc.contributor.author | 王瑞儀 | zh_TW |
dc.date.accessioned | 2021-06-17T03:45:39Z | - |
dc.date.available | 2020-02-23 | |
dc.date.copyright | 2018-02-23 | |
dc.date.issued | 2018 | |
dc.date.submitted | 2018-01-31 | |
dc.identifier.citation | [1] C. F. Quate, G. Binning, Ch Gerber, 'Atomic Force Microscope,' Physical Review Letters, vol. 56, no. 9, pp. 930-934, 1985.
[2] S. Morita, Wiesendanger, Roland, Meyer, E., Ed. Atomic Force Microscopy (Nanoscience and technology). 2002. [3] M. Hegner, Y. Arntz, 'Advanced Biosensing Using Micromechanical Cantilever Arrays, ', Ed. Atomic Force Microscopy (Biomedical Methods and Applications). 2004, pp. 39-49. [4] C. Ziegler, 'Cantilever-based biosensors,' Journal of Analytical and Bioanalytical Chemistry, vol. 379, no. 7-8, pp. 946-959, 2004. [5] T. Thundat, E. A. Wachter, S. L. Sharp, R. J. Warmack, 'Detection of mercury vapor using resonating microcantilevers,' Applied physics Letters, vol. 66 (13), no. 13, pp. 1695-1697, 1995. [6] S. P. Timoshenko, '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, vol. 41, no. 245, pp. 744-746, 1921. [7] M. Levinson, 'A new rectangular beam theory,' Journal of Sound and Vibration, vol. 74, no. 1, pp. 81-87, 1981. [8] D. L. Thomas, 'Vibration of a rectangular beam with a deforming cross-section,' Journal of Sound and Vibration, vol. 95, no. 3, pp. 397-404, 1984. [9] W. B. Bickford, 'A consistent higher order beam theory,' Developments in Theoretical and Applied Mechanics, vol. 11, no. 11, pp. 137-150, 1982. [10] J. N. Reddy, 'A simple High-order Theory for Laminated Composite Plates,' Journal of Applied Mechanics, vol. 51, pp. 745-752, 1984. [11] J. N. Reddy, C. M. Wang , K. H. Lee, 'Relationships between bending solutions of classical and shear deformation beam theories,' International Journal of Solids Structures vol. 34, no. 26, p. 1997, 1996. [12] M. Eisenberger, 'Dynamic stiffness vibration analysis using a high-order beam model,' International Journal for Numerical methods in engineering, vol. 57, pp. 1603-1614, 2003. [13] J. N. Reddy, 'Nonlocal theories for bending, buckling and vibration of beams,' International Journal of Engineering Science, vol. 45, pp. 288-307, 2007. [14] E. O. Tuck, 'Calculation of Unsteady Flows Due to Small Motions of Cylinders in a Viscous Fluid,' Journal of Engineering Mathematics, vol. 3, no. 1, pp. 29-44, 1968. [15] J. E. Sader, 'Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope,' Journal of Applied physics, vol. 84, pp. 64-76, 1998. [16] J. E. Sader, C. A. Van Eysden, 'Small amplitude oscillations of a flexible thin blade in a viscous fluid: Exact analytical solution,' Physics of Fluids, vol. 18, no. 12, 2006. [17] J. E. Sader, C. A. Van Eysden, 'Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope: Arbitrary mode order,' Journal of Applied physics, vol. 101, 2007. [18] F. J. Elmer, M. Dreier. 'Eigenfrequencies of a rectangular atomic force microscope cantilever in a medium,' Journal of Applied Physics, vol. 81, pp. 7709-7714, 1997. [19] M. K. Ghatkesar, 'Resonating modes of vibrating microcantilevers in liquid,' Journal of Applied physics, vol. 92, 2008. [20] C. Hurth, 'Hydrodynamics of oscillating atomic force microscopy cantilevers in viscous fluids,' Journal of Applied Physics, vol. 97, 2005. [21] J. N. Reddy, Energy Principles and variational methods in applied mechanics. J. Wiley and Sons, inc, 2002. [22] 陳穆璋, '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,' 碩士論文工學院應用力學研究所, 國立臺灣大學, 台北市, 2015. [23] 戴源智, '沉浸於不同液體中的梁之撓曲振動共振頻率,' 碩士論文, 工學院應用力學研究所, 國立臺灣大學, 台北市, 2016. [24] M. Aydogdu, U. Gul, 'Wave Propagation Analysis in Beams Using Shear Deformable Beam Theories Considering Second Spectrum,' Journal of Mechanics, vol. 27, 2017. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70139 | - |
dc.description.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。 | zh_TW |
dc.description.abstract | 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. | en |
dc.description.provenance | Made available in DSpace on 2021-06-17T03:45:39Z (GMT). No. of bitstreams: 1 ntu-107-R04543049-1.pdf: 2598778 bytes, checksum: 49692222e6ac9355ae5517fb7c1b7fa0 (MD5) Previous issue date: 2018 | en |
dc.description.tableofcontents | 摘要 I
Abstract II 目錄 III 圖目錄 V 表目錄 XII 符號表 XIII 1. 緒論 1 1-1 研究動機 1 1-2 文獻回顧 2 1-3 論文架構 4 2. 理論介紹 5 2-1 固體域理論 5 2-1-1 哈密爾頓原理 5 2-1-2 古典梁理論(EBT) 5 2-1-3 一階梁理論(TBT) 7 2-1-4 三階梁理論(RBT) 9 2-2 流體域理論 13 2-3 流固耦合 16 3. 求解方法 18 3-1 模態求解 18 3-1-1 古典梁-模態 18 3-1-2 一階梁-模態 20 3-1-3 三階梁-模態 25 3-2 全域函數比較 34 3-2-1 古典梁-全域函數 34 3-2-2 一階梁及三階梁-模態對頻率掃蕩 36 3-2-3 一階梁及三階梁-頻率對模態掃蕩 40 3-3 文獻比較 51 4. 結果與討論 57 4-1 長厚比 58 4-1-1 簡支梁 58 4-1-2 懸臂梁 66 4-2 材料常數比 74 4-2-1 簡支梁 75 4-2-2 懸臂梁 82 4-3 不同流體之差異比 89 4-3-1 簡支梁 90 4-3-2 懸臂梁 103 5. 結論與未來展望 116 5-1 結論 116 5-2 未來展望 117 參考文獻 118 | |
dc.language.iso | zh-TW | |
dc.title | 黏滯流體下一階及三階梁理論側向振動之模態頻率研究 | zh_TW |
dc.title | Study of the mode frequencies of flexural vibration of beam structure immersed in viscous fluids | en |
dc.type | Thesis | |
dc.date.schoolyear | 106-1 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 吳光鐘,陳世豪,沈宏俊,趙聖德 | |
dc.subject.keyword | 一階剪切梁理論,三階剪切梁理論,微懸臂梁,模態分析, | zh_TW |
dc.subject.keyword | Timoshenko beam theory,dynamic vibration of beam, | en |
dc.relation.page | 120 | |
dc.identifier.doi | 10.6342/NTU201800237 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2018-01-31 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 應用力學研究所 | zh_TW |
顯示於系所單位: | 應用力學研究所 |
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