Influence of the tip mass and position on the AFM cantilever dynamics: Coupling between bending, torsion and flexural modes

The effects of the geometrical asymmetric related to tip position as a concentrated mass, on the sensitivity of all three vibration modes, lateral excitation (LE), torsional resonance (TR) and vertical excitation (VE), of an atomic force microscopy (AFM) microcantilever have been analyzed. The effects of the tip mass and its position are studied to report the novel results to estimating the vibration behavior of AFM such as resonance frequency and amplitude of the microcantilever. In this way, to achieve more accurate results, the coupled motion in all three modes is considered. In particular, it is investigated that performing the coupled motion in analysis of AFM microcantilever is almost necessary. It is shown that the tip mass and its position have significant effects on vibrational responses. The results show that considering the tip mass decreases the resonance frequencies particularly on high-order modes. However, dislocating of tip position has an inverse effect that causes an increase in the resonance frequencies. In addition, it has been shown that the amplitude of the AFM microcantilever is affected by the influences of tip and its position. These effects are caused by the interaction between flexural and torsional motion due to the moment of inertia of the tip mass.