Dynamic analysis of AFM at air and liquid environments with considering the linear and non-linear interaction forces by Timoshenko beam model

The behavior of frequency response of the cantilever of the atomic force microscopy was different in the liquid environment in comparison with air environment. In this research, the dynamic analysis of atomic force microscopy in the air and liquid environments have been carried out with consideration of linear and non-linear interaction forces and also the effect of geometrical parameters such as length, width, height and angle between cantilever and sample's surface on the rectangular cantilever has been investigated. A rectangular beam based on the Timoshenko beam model has been simulated in ADAMS software environment and more accurate results has been received by considering the probe tip and the angle location of cantilever at simulation.At the end of the beam, a silicone tip has been considered that the applied forces on it have been approximated with two tangential and vertical springs and the vibrational simulation of cantilever at two states has been carried out with regard to linear and non-linear interaction forces.The amplitude and resonance frequency of the simulated beam based on Timoshenko model is different from obtained results of Euler beam model Due to the effect of shear deformation and rotary moment in Timoshenko beam.Therefore, the Timoshenko beam model has the better accuracy in comparison with Euler beam model.Many chemical and biological processes occurred so fast so using of short cantilever for increasing the speed of imaging at impact mode in liquid environment was very necessary. Eventually short beam that has been modeled based on Timoshenko model can produce more accurate results. This paper aimed to show that the amplitude and resonance frequency of vibration in the liquid environment were different from amplitude and frequency of vibration in the air environment due to the damping coeficient and added mass of liquid.