Microcantilever dynamics in tapping mode atomic force microscopy via higher eigenmodes analysis

Microcantilever dynamics in tapping mode atomic force microscopy (AFM) is addressed via a multimode approximation, which allows to consider external excitation at primary or secondary resonance and to highlight the effect of higher order eigenmodes. Upon presenting the AFM model and its multimode discretization, the dynamic response is investigated via numerical simulation of single- and three-mode models by considering different bifurcation parameters. Typical features of tapping mode AFM response as nonlinear hysteresis, bistability, higher harmonics contribution, impact velocity, and contact force are addressed. The analysis is conducted by evaluating damping of higher modes according to the Rayleigh criterion, which basically accounts for structural damping representative of the behavior of AFMs in air. Nominal damping situations more typical of AFMs in liquids are also investigated, by considering sets of modal Q-factors with different patterns and ranges of values. Variable attractive-repulsive effects are highlighted, along with the possible presence of a coexisting multi-periodic orbit when the system is excited at second resonance.