Dynamic Analysis of AFM in Air and Liquid Environments Considering Linear and Non-linear Interaction Forces by Timoshenko Beam Model

Abstract

The atomic force microscopy of the cantilever beam frequency response behaviour in the liquid environment is different in comparison with air environment. In this paper, the dynamic analysis of AFM in the air and liquid environments is carried out in consideration of linear and non-linear interaction forces and also the effect of geometrical parameters such as length, width, height; and inclined angle on the vibrating motion of the rectangular cantilever is investigated. A rectangular cantilever based on the Timoshenko theory is simulated in ADAMS software and more accurate results are obtained by considering the probe tip and the angular location of cantilever at simulation. At the end of the cantilever, a silicone probe is considered where the applied forces on it are approximated using two tangential and vertical springs. The vibrational simulation of cantilever at two states is carried out with regard to linear and non-linear interaction forces. The amplitude and resonance frequency of the simulated cantilever based on Timoshenko theory are different from obtained results of Euler-Bernoulli theory due to the effect of shear deformation and rotary moment in Timoshenko theory. Therefore, the Timoshenko theory has better accuracy in comparison with Euler theory. Many chemical and biological processes occur instantly; therefore the use of cantilevers with small length for improving the imaging speed at the tapping mode and in the liquid environment is essential. Eventually short cantilever that is modeled based on the Timoshenko theory may produce more accurate results. This paper is aimed to demonstrate that the amplitude and resonance frequency of vibration in the liquid environment is different from amplitude and frequency of vibration in the air environment due to the damping coeficient and added mass of liquid.