A unified necessary condition for dynamic bow snap-through with prestress tuning in electrostatically actuated...

A curved bistable microbeam, subjected to electrostatic loading from an electrode facing its concave side, may exhibit bow snap-through (BST) at nearly half the voltage ( $\approx 54\%$ ) when compared to actuation from the convex side. Previously, it was shown that introducing prestress can enable BST where it is otherwise unattainable. The current work extends the BST condition to include dynamic actuation, thus establishing dynamic bow snap-through (DBST) as a viable and sustainable form of actuation, since it can reduce actuation by $\approx$  10 to 16%. To enable analytical derivation while retaining generality across various loading scenarios, the analysis employs an undamped single-degree-of-freedom reduced-order model obtained via Galerkin's decomposition. The resulting formulation yields a necessary condition for DBST, expressed in terms of beam geometry, prestress, and initial conditions, forming a unified condition. Subsequent analysis shows that suddenly applied actuations, combined with prestress, can enable BST over a wider range of parameters, whereas excessive kinetic energy and/or prestress can suppress DBST. The proposed condition provides practical design guideline for energy-efficient, low-voltage and non-volatile bistable devices.