Periodicity and pull-in instability in current-driven magMEMS: a Sturm’s theorem approach
Skrzypacz P. Ellis G. Putek P. Pruchnik B. Dziedzic A. Abdildayev A. Onaibekov S.
17 March 2026Academic Press
Journal of Sound and Vibration
2026#625
The reliable operation of magnetic microelectromechanical systems (magMEMS) depends on the pull-in effect, which is triggered when the excitation exceeds a critical threshold value. Accurate prediction of this phenomenon under magnetostatic actuation is vital for a robust MEMS device design. This study leverages Sturm’s theorem to analyze dynamic pull-in magMEMS with current-carrying filaments, where instability typically results from the interaction between the kinetic and potential energy. The proposed method quickly determines, for a given excitation parameter, whether a periodic solution exists or pull-in occurs. Applicable to a broad range of MEMS devices, this approach supports the development of low-voltage, CMOS-compatible magnetic actuators. Findings of analytical approach are confirmed by detailed numerical illustrations. The discrepancy between three approximation methods is analyzed and discussed. The proposed algorithm is implemented in the high-level, high-performance programming language Julia. The appended codes can be easily used by MEMS designers.
Chebychev polynomial , Current-carrying filament , Dynamic pull-in , magMEMS , Periodic solution , Rational approximation , Singular oscillators , Sturm’s theorem
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School of Sciences and Humanities, Nazarbayev University, 53 Kabanbay Batyr Ave., Astana, 010000, Kazakhstan
Faculty of Electronics, Photonics and Microsystems, Wrocław University of Science and Technology, ul. Janiszewskiego 11/17, Wrocław, 50-372, Poland
School of Sciences and Humanities
Faculty of Electronics
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