Finite element simulations of nonlinear vibrations of atomic force microscope cantilevers

The analysis of the dynamic behavior of the micro-cantilevers employed in atomic force microscopy (AFM) is often limited to linear or weakly nonlinear behavior without damping. Finite element simulations are used here to study the cantilever dynamics outside of these restrictions. The nonlinear contact mechanics between the AFM tip and the material surface are modeled using the JKR model with different damping. This model is most appropriate for AFM cantilevers that are most compliant than the specimen. The focus is on the contact case in all analyses to simmplify the problem. Thus, the AFM cantilever tip is assumed to remain in contact with the specimen surface at all times during the motion. Applications for both weakly and strongly nonlinear behavior are examined. The properties of the vibration, the influence of different initial loads and different damping models on the behavior, like nonlinear shifts of the resonance frequencies, the eccentricity and asymmetry of the amplitude, of the nonlinear vibration are calculated by FEM. The numerical analysis shows that the eccentricity and the asymmetry of the amplitude are more sensitive to the change of damping and the contact stiffness than the resonance frequencies. The response of the cantilever and the evaluation of elastic properties of the sample can been studied appropriately using this model.