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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58438完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張正憲 | |
| dc.contributor.author | Shang-Yang Ting | en |
| dc.contributor.author | 丁尚洋 | zh_TW |
| dc.date.accessioned | 2021-06-16T08:15:09Z | - |
| dc.date.available | 2019-02-26 | |
| dc.date.copyright | 2014-02-26 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-02-12 | |
| dc.identifier.citation | [1]C. Ziegler, “Cantilever-based biosensors,” Analytical and Bioanalytical Chemistry, vol. 379, 946 (2004).
[2]R. Berger, E. Delamarche, H. P. Lang, C. Gerber, J. K. Gimzewski, E. Meyer, and H. J. Guntherodt, “Surface Stress in the Self-Assembly of Alkanethiols on Gold,” Science, vol. 276, 2021 (1997). [3]T. M. Battiston, J. P. Ramseyar, H. P. Lang, M. K. Baller, Ch. Gerber, J. K. Gimzewski, E. Meyer, and H. J. Guntherodt, “A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending readout,” Sensors and Actuators B, vol. 77, 122-131 (2001). [4]James W. M. Chon, P. Mulvaney, and J. E. Sader, “Experimental validation of theoretical models for the frequency response of atomic force microscope cantilever beams immersed in fluids,” Journal of Applied Physics, vol. 87, 3978 (2000). [5]X. Xu and A. Raman, “Comparative dynamics of magnetically, acoustically, and Brownian motion driven microcantilevers in liquids,” Journal of Applied Physics, vol. 102, 034303 (2007). [6]E. O. Tuck, “Calculation of unsteady flows due to small motions of cylinders in viscous fluid,” Journal of Engeering Mathematics, vol. 3, 29 (1969). [7]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, 64 (1998). [8]W. T. Thomson, Theory of Vibration with Application 4th edition Prentice Hall A Simon & Schuster Company, New Jersey, (1993). [9]W. J. Bottega, Engineering Vibrations Taylor & Francis Group, Boca Raton, (2006). [10]方同, 薛僕, 振動理論及應用 西北工業大學出版社, 西安,(1998). [11]D. A. Walters, J. P. Cleveland, N. H. Thomson, P. K. Hansma, M. A. Wendman, G. Gurley, and V. Elings, “Short cantilevers for atomic force microscopy,” Review of Scientific Instruments, vol. 67, 3583 (1996). [12]J. C. Hsu, H. L. Lee, and W. J. Chang, “Flexural vibration frequency of atomic force microscope cantilevers using the Timoshenko beam model,” Nanotechnology, vol. 18, 285503 (2007). [13]H. L. Lee, and W. J. Chang, “Effects of Damping on the Vibration Frequency of Atomic Force Microscope Cantilevers Using the Timoshenko Beam Model,” Japanese Journal of Applied Physics, vol. 48, 065005 (2009). [14]A. Sadeghi, and H. Zohoor, “Nonlinear vibration of double tapered atomic force microscope (a nano microscope) cantilevers by considering the Hertzian contact theory,” Canadian Journal of Physics, vol. 88, 5 (2010) pp 333-348. [15]A. Sadeghi, “The flexural vibration of V shaped atomic force microscope cantilevers by using the Timoshenko beam theory,” Z. Angew. Math. Mech., vol. 92, 782 (2012). [16]H. Zohoor, and A. Sadeghi, “The flexural vibration of double tapered atomic force microscope cantilevers studied by considering the contact position and using the Differential Quadrature Method,” Journal of Applied Mechanics and Technical Physics, vol. 54, 4 (2013) pp 622-635. [17]A. sadeghi, 'A new investigation for doubled tapered atomic force microscope cantilevers by considering the damping effect,' Z. Angew. Math. Mech., vol. 93, 12 (2013). [18]M. H. Korayem, and M. Damircheli, “The effect of fluid properties and geometrical parameters of cantilever on the frequency response of atomic force microscopy,” to appear in Precision Engineering, (2013). [19]S. Dohn, R. Sandberg, W. Svendsen, and A. Boisen, “Enhanced functionality of cantilever based mass sensors using higher modes,” Applied Physics Letters, vol. 86, 233501 (2005). [20]F. Lochon, I. Dufour, and D. Rebiere, “An alternative solution to improve sensitivity of resonant microcantilever chemical sensors: comparison between using high-order modes and reducing dimensions,” Sensors and Actuators B, vol. 108, 979 (2005). [21]M. K. Ghatkesar, V. Barwich, T. Braun, J. P. Ramseyer, C. Gerber, M. Hegner, H. P. Lang, U. Drechsler, and M. Despont, “Higher modes of vibration increase mass sensitivity in nanomechanical microcantilevers,” Nanotechnology, vol. 18, 445502 (2007). [22]M. K. Ghatkesar, T. Braun, V. Barwich, J. P. Ramseyer, C. Gerber, M. Hegner, and H. P. Lang, “Resonating modes of vibrating microcantilevers in liquid,” Applied Physics Letters, vol. 92, 043106 (2008). [23]黃冠榮, 微混合器與共振式微懸臂梁生物感測器的理論建立與數值模擬, 博士論文, 國立台灣大學應用力學研究所, 台北市 (2011). [24]林建豪, 微懸臂樑陣列在不同介質下的頻響函數, 碩士論文, 國立台灣大學應用力學研究所, 台北市 (2011). [25]R. D. Blevins, Formulas for Natural Frequency and Mode Shape Van Nostrand Reinhold, New York, (1979). [26]W. J. Bottega, Engineering Vibrations Taylor & Francis Group, Boca Raton, (2006) p. 634. [27]廖展誼, 微系統機械元件於流體環境中動態特性研究與原子力顯微鏡上之應用, 碩士論文, 國立台灣大學應用力學研究所, 台北市 (2010). [28]黃俊維, 微懸臂梁感測器之力學模型與最佳化設計, 碩士論文, 國立台灣大學應用力學研究所, 台北市 (2004). [29]謝瀚逸, Timoshenko和Euler懸臂梁本身及代額外微小質量在流體環境中共振頻及頻率飄移之比較, 碩士論文, 國立台灣大學應用力學研究所, 台北市 (2013) [30]Kuan-Rong Huang, Jeng-Shian Chang, Sheng D. Chao, and Kuang-Chong Wu “Beam model and the three dimensional numerical simulation on suspended microchannel resonators,” AIP advances, vol. 2, 042176 (2012) [31]Y. Song, B. “BhushanFinite-element vibration analysis of tapping-mode atomic force microscopy in liquid” Ultramicroscopy, 107 (10–11) (2007), pp. 1095–1104 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58438 | - |
| dc.description.abstract | 本文主要探討在黏滯流體環境中 Timoshenko梁的振動模型。並與Euler梁在黏滯流體環境中的振動行為分別以結構尺寸、流體環境、模態階數、剪切模數作比較。
首先介紹相關文獻，利用任意截面不可壓縮黏滯流體理論，計算流體施加在扁平梁的水力負載，再將水力函數耦合進Timoshenko梁理論中，取得流固耦合後頻率響應的求解。同時也介紹Euler梁理論流固耦合後的頻率響應。 藉由物理行為以及文獻中的結果與兩理論之間的關係相互驗證，以數值結果分別比較兩理論於不同的梁結構尺寸、不同模態階數、不同流體黏滯性、不同流體密度、不同的剪切模數之關係。以微懸臂梁作為感測器在流體環境作量測時，Timoshenko梁理論與Euler梁理論的差異會比真空中的更大，另外為了有較好的量測靈敏度需要在高模態階數下操作或是需要使用更粗短的懸臂梁時等這些情下時，使用考慮了剪切變形與轉動慣量的Timoshenko梁理論來作計算會比Euler梁理論更為妥適。 | zh_TW |
| dc.description.abstract | This paper build the vibration model of Timoshenko beam in viscous fluid. To compare the behavior with the vibration model of Euler beam in viscous fluid by the size, order of modes, fluid environment and shear modulus.
Using the Green's function to solve incompressible viscous fluid theorem of any cross-section, and to conclude hydrodynamic loading that fluid applied to the flat beam. After that, have the hydrodynamic functions coupled with the Timoshenko beam theory to obtain the frequency response function and the frequency response function which affected by the added mass after fluid-structure interaction. The Timoshenko beam numerical results are verified with the physical behavior, the relationship between the two theories and the numerical results of the reference. The numerical results of the frequency response functions were compared the relationship to two theories in different sizes of beam, different density and viscosity of fluid environment, different shear modulus, and the different order of modes. When using the micro-cantilever sensors in the fluid environment for measurement, the difference between Timoshenko beam theory and Euler beam theory will be greater than the vacuum. In addition, if we want to get the better sensitivity, we need to measure in higher mode and use the thicker beam. At such times, using the Timoshenko beam theory which considers the shear deformation and the moment of inertia can make calculations more appropriate than Euler beam theory. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T08:15:09Z (GMT). No. of bitstreams: 1 ntu-103-R00543044-1.pdf: 1633106 bytes, checksum: afecd271826c3e7afb0af8dd70d90330 (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 目錄
摘要 III Abstract IV 圖目錄 VII 表目錄 XII 符號表 XIII 第 一 章 緒論 1 1-1研究動機與目的 1 1-2文獻回顧 1 1-3論文架構 5 第 二 章 黏滯流體水力函數 6 2-1 黏滯流體下任意截面流固耦合 6 2-2 黏滯流體下扁平樑的水力負載 11 第 三 章 流固耦合振動系統與頻率響應 15 3-1 Euler梁 15 3-1-1 結構統御方程式 15 3-1-2 頻率響應及振型 17 3-1-3 流固耦合後頻率響應函數 20 3-2 Timoshenko梁 23 3-2-1 結構統御方程式 23 3-2-2 流固耦合後的共振頻率 25 3-2-3 Timoshenko梁的振型 31 第 四 章 理論驗證與數值結果 33 4-1 理論驗證 33 4-1-1 靜態分析 33 4-1-2 Timoshenko梁與Euler梁在真空環境中的比較 36 4-1-3 與文獻比較 39 4-2 數值結果 43 4-2-1流體對於振動的影響 43 4-2-2結構長度厚度比值及模態階數與流體對兩理論差異的影響 48 4-2-3流體黏滯性對兩理論差異的影響 57 4-2-4流體密度對兩理論差異的影響 66 4-2-5剪切模數對結構與兩理論差異的影響 75 第 五 章 結論及未來展望 84 5-1結論 84 5-2未來展望 86 參考文獻 87 附錄 91 | |
| dc.language.iso | zh-TW | |
| dc.subject | Euler梁理論 | zh_TW |
| dc.subject | Timoshenko梁理論 | zh_TW |
| dc.subject | 頻率響應 | zh_TW |
| dc.subject | 振動 | zh_TW |
| dc.subject | 原子力顯微鏡 | zh_TW |
| dc.subject | 微懸臂梁感測器 | zh_TW |
| dc.subject | 黏滯流體 | zh_TW |
| dc.subject | viscous fluid | en |
| dc.subject | micro-cantilever beam sensor | en |
| dc.subject | atomic force microscope | en |
| dc.subject | Euler beam theory | en |
| dc.subject | Timoshenko beam theory | en |
| dc.subject | frequency response | en |
| dc.subject | vibration | en |
| dc.title | Timoshenko和Euler懸臂梁在流體環境中共振頻之比較 | zh_TW |
| dc.title | Comparisons of Resonant Frequency between Timoshenko and Euler Cantilever Beam Immersed in the Fluid Environments | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 吳光鐘,黃冠榮,陳世豪 | |
| dc.subject.keyword | 微懸臂梁感測器,原子力顯微鏡,振動,頻率響應,Timoshenko梁理論,Euler梁理論,黏滯流體, | zh_TW |
| dc.subject.keyword | micro-cantilever beam sensor,atomic force microscope,vibration,frequency response,Timoshenko beam theory,Euler beam theory,viscous fluid, | en |
| dc.relation.page | 93 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-02-13 | |
| 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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