Abstract
We study the dynamical behavior of electromagnetically actuated MEMS cantilevers used in atomic force microscopy (AFM) in the non-contact working state. The nonlinear nature of the MEMS sensor’s tip-sample interaction, considered in the dynamic operation mode, must be appropriately modeled due to the van der Waals-type attraction/repulsion force. The resulting one-degree-of-freedom lumped parameter model constitutes the initial value problem for singular oscillator equation. The occurrence of pull-in solutions for this model with one magnetic excitation parameter is thoroughly analyzed. In particular, due to the Lorentz force-based electromagnetic actuation, we investigate two dynamic pull-in scenarios corresponding to a nonlinear system for which pull-in thresholds are analytically determined. Moreover, sufficient conditions for occurrence of pull-in or oscillatory solutions are rigorously derived and validated numerically. These results generalize those given previously, and can be useful for designing single-degree-of-freedom models of electromagnetically actuated MEMS cantilevers. Finally, we present and discuss a comparison between experimental data and theoretical predictions for a defined benchmark case.