Flexural Vibration of Atomic Force Microscope Cantilever with Dimensional Effects

Atomic Force microscope (AFM) is one of the powerful and useful tools in nanoscale science and technologies with applications from surface characterization in material science, to the study of living biological systems in their natural environment. AFM operate in three modes of contact, non-contact and tapping mode. In this paper, by focusing on the development of a more comprehensive model of an AFM micro-cantilever beam, considering the effects of mass and rotary inertia of the tip using Euler-Bernoulli beam theory is considered. The comparison of the present results and the results of other investigators, which has been done in case studies, generally shows a very good agreement. The results show that the effect of mass and rotary inertia of the tip depending on its dimensions is important and should be considered. Finally, the effects of cantilever inclination and tip height on the resonance frequencies are also examined.