Dynamic bow snap-through in electrostatically actuated microbeams under prestress tuning

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 $\approx \! 10 \! - \! 16\%$. 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 guidance for energy-efficient, low-voltage and non-volatile bistable devices.一面朝向凹面的电极对曲面双稳态微梁施加静电载荷时，该微梁的弓形跳变（bow snap-through, BST）触发电压仅约为凸面驱动时的54%，接近原驱动电压的一半。已有研究表明，引入预应力可在原本无法实现BST的工况下促成该现象。本研究将BST的触发条件拓展至动态驱动场景，由此确立动态弓形跳变（dynamic bow snap-through, DBST）作为一种高效可持续的驱动形式，其可将驱动电压降低约10%~16%。为在保留各类载荷场景普适性的前提下实现解析推导，本研究采用通过伽辽金分解得到的无阻尼单自由度降阶模型开展分析。所得到的公式推导给出了DBST的必要条件，该条件以微梁几何参数、预应力及初始条件为变量，形成统一的判定准则。后续分析表明，突加驱动与预应力结合可使BST的适用参数范围大幅拓宽，而过高的动能和/或预应力则会抑制DBST的发生。本研究提出的判定准则可为节能、低电压且非易失性双稳态器件的实际设计提供实用的设计指导。