Necessary conditions for static and dynamic bow snap-through in electrostatically actuated initially curved and latched micro-beams

Abstract

A curved bistable micro-beam, subjected to electrostatic loading from an electrode facing its concave side, may produce a snap-through response with voltages as low as 54%, when compared to actuation from a convex facing electrode. Such actuation has been dubbed “bow actuation” due to the similarity of preloading an arrow onto a bow, and the resulting equilibrium shift, as “bow snap-through”. Under a certain elevation-to-thickness ratio, a bistable beam will also become latchable, allowing the beam to maintain itself in its second stable state under zero load/voltage. In the current work, necessary conditions are found for static and dynamic bow snap-through, which can be used as a tool to design and produce bow snap-through responses, promoting efficient non-volatile and low-power consumption bistable based devices. The conditions are found using an undamped dynamic single degree-of-freedom (DoF) reduced-order (RO) model, attained via Galerkin’s decomposition. Subsequent numerical calculations, conducted in the presence of ambient damping, show that the condition is necessary to attain bow snap-through responses, while also disclosing the snapping behaviour of the model.