Mahdavi M H, Farshidianfar A, Tahani M, Mahdavi S, Dalir H
Department of Mechanical Engineering, Ferdowsi University of Mashhad, PO Box 91775-1111, Mashhad, Iran.
Ultramicroscopy. 2008 Dec;109(1):54-60. doi: 10.1016/j.ultramic.2008.08.003. Epub 2008 Aug 22.
This paper focuses on the development of a complete model of an atomic force microscope (AFM) micro-cantilever beam, based on considering the effects of four major factors in modeling the cantilever. They are: rotary inertia and shear deformation of the beam and mass and rotary inertia of the tip. A method based on distributed-parameter modeling approach is proposed to solve the governing equations. The comparisons generally show a very good agreement between the present results and the results of other investigators. As expected, rotary inertia and shear deformation of the beam decrease resonance frequency especially at high ratio of cantilever thickness to its length, and it is relatively more pronounced for higher-order frequencies, than lower ones. Mass and rotary inertia of the tip have similar effects when the mass-ratio of the tip to the cantilever is high. Moreover, the influence of each of these four factors, thickness of the cantilever, density of the tip and inclination of the cantilever on the resonance frequencies has been investigated, separately. It is felt that this work might help the engineers in reducing AFM micro-cantilever design time, by providing insight into the effects of various parameters with the micro-cantilever.
本文重点在于建立原子力显微镜（AFM）微悬臂梁的完整模型，该模型在建立过程中考虑了四个主要因素的影响。这四个因素分别是：梁的转动惯量和剪切变形以及针尖的质量和转动惯量。提出了一种基于分布参数建模方法来求解控制方程。总体比较结果表明，本文结果与其他研究者的结果非常吻合。正如预期的那样，梁的转动惯量和剪切变形会降低共振频率，尤其是在悬臂厚度与长度之比很高时，并且对于高阶频率而言，这种影响比低阶频率更为明显。当针尖与悬臂的质量比很高时，针尖的质量和转动惯量具有类似的影响。此外，还分别研究了这四个因素中的每一个，即悬臂的厚度、针尖的密度以及悬臂的倾斜度对共振频率的影响。人们认为，这项工作通过深入了解各种参数对微悬臂梁的影响，可能有助于工程师缩短AFM微悬臂梁的设计时间。
