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The mathematical model of an AFM nonuniform probe in the modified couple stress theory is derived here. The analytical method is proposed to design the configuration of the AFM probe satisfying the integer-multiples relation among frequencies. The varying cross-section of the probe is tuned to match the specific requirement. One discovers two similarity conditions such that the integer-multiples relation is kept in spite of the size-dependency parameter. Moreover, the relations among the natural frequencies, the effective spring constant and the geometry parameters are discovered. The specific frequencies and spring constant can be obtained by tuning the probe parameters via the relations.

Size-dependency effect on design of harmonic AFM probe in the modified couple stress theory