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

Theoretical Analysis on Dynamic Characteristics of Micromechanical Components in the Fluid Environment and Application of Atomic Force Microscopy

廖展誼(Zhan-Yi Liao)

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(2010年)

https://doi.org/10.6342/NTU.2010.02077

摘要

本文探討流體環境中梁結構受到周圍牆壁影響的動態特性。首先藉由尋找Reynolds方程式與Euler梁振動方程式之間的耦合關係，推導兩種不同的分析求解方法：頻率響應法和格林函數法，以獲得系統振動行為的物理量，如共振頻率、頻率偏移和阻尼比等參數，並且交叉比對實驗數據與數值模擬來比較兩種方法的異同，發現頻率響應法對於流-固系統振動行為評估有較好的準確性。
文章中建立流-固振動系統分析流程，獲得相關物理參數：等效質量、等效勁度與等效阻尼，識別判斷系統之中各項材料性質以及牆效應對流-固耦合系統動態特性產生之影響，以便瞭解流體環境、牆效應與結構振動行為間交互作用的關係。
最後使用本文所提出的流-固系統理論，描述原子力顯微鏡在流體環境中，非接觸掃瞄模式懸壁探針的作動行為，探討懸臂探針其長度之設計規範，並且說明若式儀器使用尖端長度過短的探針量測，會受到流場行為與牆效應干擾而導致能量消散情況嚴重，造成共振頻率判斷不易，進而使得量測失真。

關鍵字

振動 ； 流固耦合 ； 微系統動態特性 ； 原子力顯微鏡

並列摘要

This paper mainly investigates the dynamic characteristics of the beam structure located at the neighborhood of the wall inside the chamber filled with different fluids. Firstly, by establishing the relation between the Reynolds equation and Euler beam equation, it is derived for two analytic approaches: Curve fitting and Green's function method, so that specific dynamic characteristics of the entire system involving the resonant frequency, frequency shift, and damping ratio can be acquired. Compared with the differences between the two analytic methods by a cross checking of experimental data and numerical simulation, the expected vibration behavior of the entire system evaluated by Curve fitting method has the higher accuracy.
Secondly, based on calculated dynamic characteristics including the resonant frequency, frequency shift, and damping ratio, corresponding to the frequency response of single degree of freedom system, effective mass, damping and stiffness can be evaluated for the beam structure connecting with the still fluid and the chamber wall, and the coupling dynamic reaction can be comprehended by discussing these extended physical parameters.
Finally, the preceding analytic procedure is used to demonstrate the limitation on a tip length of a probe of a non-contact mode atomic force microscope coupled with the fluid environment and the measured samples, and provide the suggestion of the range in the design of probe tips.

並列關鍵字

vibration ； atomic force microscope ； fluid-structure interaction

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