Timoshenko 和Euler 懸臂梁本身及帶額外微小質量在流體環境中共振頻及頻率飄移之比較

Comparisons of Resonant Frequency and Resonant Frequency Shift due to the Added Mass between Timoshenko and Euler Cantilever Beam Immersed in the Fluid Environments

謝瀚逸(Han-Yi Hsieh)

指導教授 ： 張正憲

國立臺灣大學/工學院/應用力學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.00033

摘要

本文主要建立Timoshenko 梁於黏滯流體中的振動模型。並將之與Euler 梁於黏滯流體中振動行為以尺寸、流體介質種類、模態階數分類比較，最後將額外質量對於兩理論頻率偏移之影響做比較。
本文首先介紹相關文獻，利用格林函數解析任意截面不可壓縮黏滯流體理論，得出流體施加在扁平梁的水力負載，再將水力函數分別耦合進Euler 梁理論與Timoshenko 梁理論中，取得流固耦合後的頻率響應函數及受額外質量影響的頻率響應函數。
藉由物理行為、兩理論之間的關係以及與文獻中數值結果相互驗證。以數值結果分別比較兩理論於不同尺寸、不同流體介質、不同模態階數之關係。最後同樣以數值結果得知額外質量對兩理論於流體環境中振動之共振頻率的影響。感測器常於流體環境中做量測，由於其頻率於高模態時流體對結構的影響較小，且Timoshenko 梁理論與Euler 梁理論於高模態時差異越趨明顯，本文中之數值結果
呈現當L h

關鍵字

微懸臂梁感測器 ； 原子力顯微鏡 ； Timoshenko 梁理論 ； Euler梁理論 ； 黏滯流體 ； 振動 ； 頻率響應

並列摘要

This thesis is primarily based vibration model of Timoshenko beam in viscous fluid. To compare the vibration model with the vibration behavior of Euler beam in viscous fluid by the size, fluid type and modal order. In the end of the comparison, the added mass effect of two theoretical frequency shifts is compared.
This thesis firstly introduces the relevant reference. 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 Euler beam theory and Timoshenko beam theory to obtain the frequency response function and the frequency response function which affected by the added mass after fluid-structure interaction.
Ultimately, 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, different fluids, and the different modal orders. Finally, we can find out the added mass effect of resonant frequency which vibrates in the fluid environment of the two theories by the numerical results.
Sensors often do measurements in the fluid environment. Because the effect of the frequency is smaller when the fluid acting on the structure, and the differences of Timoshenko beam theory and Euler beam theory become more obvious in high mode. The numerical results in this paper present that the difference in 8th mode is up to 65% when L/ h

並列關鍵字

microcantilever beam sensor ； atomic force microscope ； Timoshenko

參考文獻

[22] 林建豪, 微懸臂梁陣列在不同介質下的頻響函數, 碩士論文, 國立台灣大學

[26] 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

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