Bow Snap-Through Necessary Condition in Electrostatically Actuated Initially Curved and Latched Micro-Beams

Abstract

Abstract A curved bistable micro-beam, subjected to electrostatic loading from an electrode facing its concave side, may produce a snap-through response with almost half the voltage when compared to actuation emanating from an electrode facing the convex side of the beam. Such actuation has been dubbed “bow actuation” due to the similarity of preloading an arrow onto a bow, and the resulting shift in equilibrium. Under a certain elevation-to-thickness ratio, a bistable beam will also become latchable, possessing a zero point load (i.e., latching point), which allows the beam to maintain itself in its second stable state under zero load/voltage. In the current work, a necessary condition is found, describing the geometry and initial conditions required for static bow snap-through response. The condition allows one to design and produce a bow snap-through that will enable the beam to converge to its latching point, thus promoting efficient non-volatile, and low-power consumption bistable-based devices. The condition is 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, while also disclosing the behaviour of the model.