Global Limit Points Behaviour and Global Tristable Thresholds in Electrostatically Actuated and Weakly Coupled Double Micro-Beam Structures

Abstract The study presents, for the first time, a rigorous global stability analysis of a weakly coupled electrostatically actuated double micro-beam structure using a reduced-order (RO) model, derived via Galerkin’s decomposition. The global stability of the structure is determined by using eigenvalue analysis of the double-beam system, extended to isolate and thereby extract global limit points from equilibrium curves, which do not necessarily coincide with their extremum points. The study is carried out in two stages. First, the structure is studied when it is mechanically loaded to establish the analysis paradigm, while also serving as a validation tool where a finite element (FE) model is used as the reference. For the electrostatic load, finite differences (FD) direct solutions were used as the reference after establishing their merit under the previous load. It is shown that while a double micro-beam can have limit point behaviour dominated by bistability, it will transform under an electrostatic load to reveal hitherto unknown complex limit point maps, comprising of tri-, quad- and quintstable configurations, along with abrupt branch formations, unobserved in single curved beams. The RO model shows it can be used to project stability shifts of the structure and used as a tool to design compact tristable actuators and devices.