Analysis of dynamic pull-in for lumped MEMS model of atomic force microscope with constant magnetic excitation
Skrzypacz P.S. Putek P.A. Pruchnik B.C. Turganov A. Ellis G.A. Gotszalk T.P.
24 November 2025Academic Press
Journal of Sound and Vibration
2025#617
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 sensors 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.
AFM , Dynamic pull-in , MagMEMS , MEMS , Periodic solutions , Singular oscillators
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School of Sciences and Humanities, Mathematics Department, Nazarbayev University, 53 Kabanbay Batyr Ave., Astana, 010000, Kazakhstan
Wrocław University od Science and Technology, Faculty of Electronics, Photonics and Microsystems, ul. Janiszewskiego 11/17, Wrocław, 50-372, Poland
School of Sciences and Humanities
Wrocław University od Science and Technology
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