The effect of surfaces type on vibration behavior of piezoelectric micro-cantilever close to sample surface in a humid environment based on MCS theory

Atomic force microscopy (AFM) has been known as an innovative tool in the fields of surface topography, determination of different mechanical properties and manipulation of particles at the micro- and nanoscales. This paper has been concerned with advanced modeling and dynamic simulation of AFM micro-cantilever (MC) in the amplitude mode in the air environment. To increase the accuracy of the governing equations, modified couple stress theory appropriate in micro- and nanoscales has been utilized based on Timoshenko beam theory in the air environment near the sample surface. Also, to discretize the equations, differential quadrature method has been recommended. In modeling, geometric discontinuities due to the presence of a piezoelectric layer enclosed between two electrode layers and the change in MC cross section when connected to the MC have been considered. In addition to the effect of MC modeling on the accuracy of modeling and vibration amplitude during surface topography, understanding and modeling the environmental forces in the air environment, including van der Waals, capillary and contact forces, are important. This paper has been provided more accurate environmental forces modeling and has been investigated the vibration behavior of piezoelectric MC in the humid environment. Moreover, this paper has been examined the maximum and minimum MC amplitude in the air environment close to the surface with different kinds of topography. The results illustrate that kind of surfaces has effect on the maximum and minimum amplitude due to the decrease or increase in equilibrium MC distance.