Global limit points behaviour and multistable thresholds in electrostatically actuated double micro-beam structures

The study presents a rigorous global stability analysis of a weakly coupled and electrostatically actuated double micro-beam structure. The analysis is conducted using a reduced-order (RO) model, from which an eigenvalue analysis is carried, to determine stable and unstable points along a given equilibrium curve, thus providing stable and unstable branches, that are differentiated by limit points. Under such an analysis, it is found that unlike classical structures, limit points will not necesserally coincide with extremum points in a given curve. In the current study, the analysis is extended to a range of parameters to create a global stability analysis, prompting global limit points maps, used to determine their evolution, as well as determine various stability thrsholds. The study is carried out in two stages. First, it is studied when the structure is mechanically loaded, solidifying the analysis paradigm while also serving as a preliminary validation tool, where a finite element (FE) model serves as the reference. The analysis then moves to study the effect of electrostatic load, where direct solutions of finite differences (FD) were used as the reference, after establishing their merit at the previous stage. It is shown that while a double micro-beam can become bistable when mechanically loaded, it will transform under electrostatic load to include hitherto unknown complex limit point maps, prompting tri-, quad- and quintstability, alongside new dynamic configurations, as well as unorthodox branch formations. It is shown that the model can project stability shifts of the structure and be used as a design tool for compact tristable actuators.