Static, eigenvalue problem and bifurcation analysis of MEMS arches actuated by electrostatic fringing-fields

In this work, we investigate the structural behavior of a micro-electromechanical system arch microbeam actuated by electric fringing-fields where the electrodes are located at both side of the microbeam. In this particular configuration, the electrostatic actuating force is caused by the asymmetry of the fringing electric fields acting in a direction opposite to the relative deflection of the microbeam. A reduced-order model 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 any structural instability. The eigenvalue problem is then investigated to calculate 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 structural instability. The results show elimination of the so-called pull-in instability in this kind of systems as compared to the regular case of parallel-plates electrostatic actuation. The bifurcation analysis shows that the arch goes for asymmetric bifurcation (symmetry breaking) with increase in initial elevation without the occurrence of symmetric bifurcation (snap-through) for any initial elevation.