Optimizing dynamic pull-in threshold and periodic trajectories for magnetically actuated MEMS (magMEMS) in wearable sensors

Magnetically actuated micro-electro-mechanical systems (magMEMSs) are pivotal for wearable sensor applications that need high sensitivity, fast response, and compact integration, such as biomedical monitoring and motion-tracking devices. In this paper, we investigate the dynamic pull-in instability and periodic trajectory analysis of magMEMS models with current-carrying filaments, addressing critical challenges in a miniaturized sensor design. A simplified Galerkin approach is used to analyze a Lorentz-force-driven MEMS oscillator, deriving approximate expressions for the dynamic pull-in threshold—a key criterion for stable periodic operation—and the corresponding oscillation frequency and periodic solutions. Extensive numerical simulations support and validate the analytical results. These findings offer valuable insights to assist in the design and optimization of MEMS devices in wearable sensors.