Analysis of the atomic force microscopy vibration behavior using the Timoshenko theory by multi-scale method in the air environment.

This article deals with the modeling and simulation of the vibration behavior of piezoelectric micro-cantilever (MC) based on the Timoshenko theory and using multi-scale (MTS) method in the air environment. In this regard, the results are compared with the previous literature, such as the finite element method and the MTS method. The analysis of the piezoelectric MC vibrating behavior is investigated in a dynamical mode including non-contact and tapping modes. The dynamics of this system is affected by interferential forces between probe tip and sample surface, such as van der Waals, capillary, and contact forces. According to the results, the forces applied to the probe tip reduce the amplitude and the resonance frequency. The simulation of surface topography in non-contact mode and tapping for rectangular and wedge-shaped roughness in the air environment are presented. Various experiments have been conducted in Ara research Company using the atomic force microscopy device in the amplitude mode. In the NSC15 Cantilever, the first natural frequency is derived from the results of the MC simulation based on Timoshenko beam theory, the practical results are 295.85 and 296.12 kHz, and the error rate is 0.09; at higher natural frequencies, the error rate has been increased. The γ coefficient is a measure of the nonlinear effects on the system; the effect of the piezoelectric length and width on γ coefficient is also investigated.