Assessment of different theories about size dependency effect on the resonant frequency of an AFM subjected to van der Waals force

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The size-dependent effect on the dynamic behavior of the structures in the order of microns or sub-microns is significant. The mathematical models of the AFM probe subjected to van der Waals force based on three different theories are presented and solved. The numerical results by the perturbation method in modified strain gradient theory and the experimental results are very consistent. The resonant frequency-material length scale parameter relation relationships among the three models are discovered. According to the relationships, the resonant frequencies can be easily and accurately predicted.