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

Abstract

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.

Keywords:

• AFM
• classical theory
• modified couple stress theory
• modified strain gradient theory
• frequency shift
• perturbation method
• resonant frequency-material length scale parameter relation

Additional information

Funding

The support of the Ministry of Science and Technology of Taiwan, R. O. C., is gratefully acknowledged (Grant number: MOST 108-2221-E-168-009).