Periodicity and pull-in instability in current-driven magMEMS: a Sturm’s theorem approach

• magMEMS prototype driven by current-carrying filaments • Analysis of magMEMS oscillator model with damping term • Detection of pull-in or periodic solutions by using Sturm’s Theorem • Numerical illustrations of theoretical findings using Julia code • Valuable insights for MEMS designers without time-consuming finite element analysis 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 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.