Unified dynamic bistability criteria in electrostatically actuated curved prestressed microbeams

Abstract

In this study, a set of criteria, which defines the appearance of dynamic bistability in curved beams is formulated and validated. Such a form of bistability can appear in curved microstructures when subjected to nonlinear, displacement-dependent, electrostatic load, prompting three limit points, but with an orientation that will not allow for a snap-through response via a quasi-static load. Since a snap-through response is achievable only via a specific dynamic loading sequence, such a configuration was dubbed as “dynamically bistable”. The present study aims at finding the threshold at which electrostatically pre-stressed curved microbeams can manifest dynamic bistability. In addition, since the presence of a bifurcation can hinder dynamic bistability, symmetry breaking was taken into account, providing a sufficient condition in the presence of an asymmetrical snap-through response. The conditions were derived using a single and two degrees-of-freedom (DoFs) reduced-order (RO) models, found via Galerkin’s method, adding two new conditions to the configuration phase space of electrostatically actuated microbeams. The result is a set of two conditions, one necessary and one sufficient, including upper and lower boundaries, thus forming a unified set of criteria for the emergence of dynamic bistability. The study concludes with validation conducted against direct solutions taken from finite differences (FD) based calculations, as well as against experimental results obtained in a previous study.