Static and bifurcation analysis of MEMS arches actuated by electrostatic fringing fields

In this work, we investigate a micro-electromechanical system (MEMS) arch microbeam actuated by fringing electric field where the electrodes are located at both side of the microbeam. An electrostatic force caused by asymmetry of the fringing electric fields acts in a direction opposite to the relative deflection of the microbeam, resulting in a restoring electrostatic force which increasing with the applied DC voltage. A reduced-order model (ROM) is derived for the considered system using the so-called Galerkin decomposition and assuming linear undamped mode shapes of a straight beam as basis functions in the decomposition process. A static analysis is performed to investigate the occurrence of the snap-through instability. The eigenvalue problem is then investigated to obtain the fundamental as well as higher natural frequencies variation of the microbeam with the applied DC load. A bifurcation analysis is then implemented to derive a criterion for whether symmetric or asymmetric bifurcation is occurring during the static snap-through instability. The results show elimination of the so-called pull-in instability in this kind of systems as the stationary electrodes are located on either sides rather than at the bottom as in case parallel plate actuation. This system can be useful to design pull-in free MEMS bi-stable devices.