Abbasi Mohammad, Karami Mohammadi Ardeshir
Engineering Department, School of Mechanical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran.
Microsc Res Tech. 2015 May;78(5):408-15. doi: 10.1002/jemt.22488. Epub 2015 Mar 9.
A relationship based on a nonlocal elasticity theory is developed to investigate the torsional sensitivity and resonant frequency of an atomic force microscope (AFM) with assembled cantilever probe (ACP). This ACP comprises a horizontal cantilever and a vertical extension, and a tip located at the free end of the extension, which makes the AFM capable of topography at sidewalls of microstructures. First, the governing differential equations of motion and boundary conditions for dynamic analysis are obtained by a combination of the basic equations of nonlocal elasticity theory and Hamilton's principle. Afterward, a closed-form expression for the sensitivity of vibration modes has been obtained using the relationship between the resonant frequency and contact stiffness of cantilever and sample. These analysis accounts for a better representation of the torsional behavior of an AFM with sidewall probe where the small-scale effect are significant. The results of the proposed model are compared with those of classical beam theory. The results show that the sensitivities and resonant frequencies of ACP predicted by the nonlocal elasticity theory are smaller than those obtained by the classical beam theory.
基于非局部弹性理论建立了一种关系，以研究带有组装悬臂探针（ACP）的原子力显微镜（AFM）的扭转灵敏度和共振频率。这种ACP包括一个水平悬臂和一个垂直延伸部分，以及位于延伸部分自由端的一个尖端，这使得AFM能够对微结构的侧壁进行形貌测量。首先，通过非局部弹性理论的基本方程与哈密顿原理相结合，得到了用于动态分析的运动控制微分方程和边界条件。随后，利用悬臂和样品的共振频率与接触刚度之间的关系，得到了振动模式灵敏度的闭式表达式。这些分析更好地描述了具有侧壁探针的AFM的扭转行为，其中小尺度效应显著。将所提出模型的结果与经典梁理论的结果进行了比较。结果表明，非局部弹性理论预测的ACP的灵敏度和共振频率小于经典梁理论得到的结果。
