微懸臂梁陣列在不同介質下的頻響函數

Abstract

本文主要探討在無黏流體及黏滯流體下多樑陣列振動影響。藉由相關文獻的結果得到不同流體下的頻響函數並比對陣列與單樑的振動行為，進行觀察與比較其差異。 本文首先介紹相關文獻，藉由勢流理論推導不可壓縮無黏流體理論，得出流體賦予圓柱結構的水力負載；以及利用格林理論解析任意截面不可壓縮黏滯流體理論，得出流體施加在無厚度扁平樑的水力負載。最後使用尤拉樑結構振動理論，將水力函數耦合至結構振動中，以獲取流固耦合後的頻響函數。 為了驗證數值模擬的結果是否與上述理論相符，本研究針對兩種流體理論進行驗證。除了將理論重現外，在無黏流體下，利用有限元素軟體ANSYS針對陣列的各種系統模態頻率進行驗證。並利用模擬做幾何轉換，將圓柱轉換為我們所關注的扁平梁來進行分析；在黏滯流體下，藉由將樑陣列拉遠會近似單樑的狀況，分別利用單樑理論、單樑近似解及多樑理論，進行交叉驗證。 經過驗證後，同時比較相位差、振幅比及間距比對扁平樑浸入不同流體下頻響函數的影響，結果顯示主要的參數影響為間距比。分析之後的結果發現在無黏流體中雙樑交互影響降低至5%需要在間距比0.41以上；在黏滯流體中間距比則須在0.59以上。

The interaction of micro-cantilever array vibration in inviscid and viscous fluid was demonstrated in this report. Comparatively vibration between array and single beam is based on response frequency in different fluid. First, two kind incompressible fluid theorem are introduced, which develop already. The inviscid theorem is solved by potential theorem which finds the hydrodynamic loading in circular section. Therefore, the viscous theorem is solved by Green’s function, also finds hydrodynamic loading but in zero thickness flat section. Hydrodynamic loadings in different fluid are coupled into structural by utilizing Euler beam vibration theory. Finally, the coupled frequency responses are acquired. Second, follow the interest in theorem we discussed are matched by analytic simulation. The coupled nature frequencies in inviscid fluid are verified by FEM simulation, and change the geometry into flat cantilever beam array in accordance with we expect. To verify the viscous theorem, three theorems are exploited, single beam theorem, single approximate solution, and array theorem. There has an assumption that the cantilever array separate far enough will similar to a single beam. Finally, the mainly physical parameter is gap ratio, which is found by consider the impact of change phase shift, amplitude ratio and gap ratio, that the flat beam array vibrate in viscous fluid. The influence of couple interaction has been detected that will reduce to 5%, the gap ratio must be above 0.41 in inviscid fluid and 0.59 in viscous fluid.