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In this paper, the effect of size of an atomic force microscope (AFM) with an assembled cantilever probe (ACP) on resonant frequencies and their sensitivities are investigated using the strain gradient elasticity theory. The proposed ACP comprises a horizontal microcantilever, an extension and a tip located at the free end of the extension, which make the AFM capable of scanning the sample sidewall. First, the governing differential equation of motion and boundary conditions for dynamic analysis are obtained by a combination of the basic equations of the strain gradient elasticity theory and Hamilton principle. Afterwards, the flexural resonant frequency and sensitivity of the proposed AFM microcantilever are obtained numerically. The results of the proposed method are compared with those of modified couple stress and classical beam theories. The comparison shows that the difference between the results predicted by the strain gradient elasticity theory with those obtained by couple stress and classical beam theories become significant when the horizontal cantilever thickness comes approximately close to the material length scale parameter.

Keywords: Atomic force microscope, Assembled Cantilever Probe, Strain gradient elasticity theory, Modified couple stress theory

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