Micromechanical systems (MEMS) based on electrostatic actuators are commonly involved in driving and actuating high-speed micro-structures. For this to be efficient, these micro-actuators must produce sufficient actuating force in order to achieve the required large strokes for such operations (usually in the order of tens of microns). However, this larger amount of displacement will require high actuation electrostatic voltages (typically in the order of hundreds of volts) or larger actuator dimensions, resulting in a bulky and inefficient design. To overcome these challenges, this paper examines the possible use of the snap-through instability in an electrostatically actuated and initially curved (shallow arch) clamped-clamped microbeam actuator arrangement. An extended version of the variational Hamilton principle is applied to derive nonlinear equations governing the steady-state behavior of the structure under step DC load. These equations are solved by effectiveness meshless numerical Galerkin decomposition technique. A convergence study is performed to show the effectiveness and advantages of the applied numerical approach to the formulated nonlinear problem. The investigation inspects different initial curvature profiles (first three symmetric buckled modes: first, third, and fifth modes) for the shallow arch. It was reported that the presence of the snap-through instability, for all investigated initial profiles, in the structural behavior of the micro-actuator produces a non-trivial order of magnitude increase in its resultant displacement as compared to the classical parallel-plate actuator with identical geometrical dimensions and operating conditions. In addition, out of the assumed first three symmetric buckled modes to outline the initial curvature of the shallow arch microbeam, only the first and fifth modes showed a strong impact on the micro-actuator performances.

基于静电致动器的微机械系统 (MEMS) 通常涉及驱动和驱动高速微结构。为了使其有效，这些微致动器必须产生足够的致动力以实现此类操作所需的大冲程（通常为数十微米的数量级）。然而，这种较大的位移量将需要高驱动静电电压（通常在数百伏的数量级）或更大的驱动器尺寸，从而导致设计笨重且效率低下。为了克服这些挑战，本文研究了在静电驱动和最初弯曲（浅拱形）夹钳微束致动器装置中可能使用快速通过不稳定性。应用变分哈密顿原理的扩展版本来推导控制阶跃直流负载下结构稳态行为的非线性方程。这些方程通过有效的无网格数值伽辽金分解技术求解。执行收敛性研究以显示应用数值方法对公式化非线性问题的有效性和优势。调查检查了浅拱的不同初始曲率轮廓（前三个对称屈曲模式：第一、第三和第五模式）。据报道，对于所有研究的初始轮廓，存在快速通过的不稳定性，与具有相同几何尺寸和操作条件的经典平行板致动器相比，微致动器的结构行为在其合成位移中产生了非平凡的数量级增加。此外，在描绘浅拱微梁初始曲率的前三个对称屈曲模式中，只有第一和第五模式对微执行器性能有强烈影响。