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A hybrid full-Lagrangian technique for the static and dynamic analysis of magnetostatic MEMS

Magnetostatic microelectromechanical systems (MEMS) are based on the electromagnetic interactions between magnetic microstructures and active (coils) or passive (permanent magnets) magnetic field sources. They offer distinct advantages at the micrometer scale in strength, polarity and distance of actuation, when compared to other methods of actuation in MEMS. For proper understanding and detailed exploration of magnetostatic MEMS, it is important to have a reliable and efficient physical level simulation tool. In this paper, we propose an efficient technique, namely the hybrid full-Lagrangian technique for the static and dynamic analysis of magnetostatic MEMS. In this technique, the magnetostatic analysis needed to compute the magnetostatic force acting on the microstructure is performed using a hybrid BIE/Poisson approach. The Poisson equation is solved for the interior magnetostatic domains and the boundary integral equation (BIE) formulation of the potential equation is solved for the exterior magnetostatic domain and the different domains are coupled through interface conditions. A Lagrangian description of all the physical domains (magnetostatic, mechanical and fluidic) is used to eliminate geometry updates and rediscretization. The Lagrangian formulation along with the hybrid approach makes the proposed technique much more efficient than conventional tools for the analysis of magnetostatic MEMS. The new technique is used to simulate several magnetostatic MEMS switches and relays and validated by comparing numerical simulation results with experimental data. Dynamic analysis of a magnetostatic MEMS switch is performed using the new technique.