本文提出一個解法，可以求出原子力顯微鏡(AFM)之V型微探針在非線性原子力邊界條件下之確切靜態撓度，另外也求出在彈性邊界與薄膜阻尼下的動態解。首先考慮一般情況下的探針物理模型，推導出其統御方程式和邊界條件。再分別討論靜態位移和動態共振頻率，由於V 型樑的特殊造型，用連續條件求出系統的正解。研究探針-樣品表面間之非線性力作用與探針撓度的關係、各種參數對系統靈敏度之影響；非接觸量測模式(non-contact mode)之尺寸改變與薄膜阻尼對共振頻率影響的問題。

　　A new method is proposed to drive exact static deflection of AFM (atomic force microscopy) V-shaped probe with nonlinear atomic force boundary, and dynamic natural frequency with elastic root and squeeze film damping. First, drive the governing equation and boundary conditions of a general physical model. And discuss static deflection and dynamic resonance frequency respectively. Use continuity condition to derive the solution due to the geometry of V-shaped cantilever tip.
　　Investigate the influence of natural frequency shifting by probe dimension in the non-contact model, the relation between deflection of beam and tip-surface distance, and the influence of sensitivity of measurement by some parameters.

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