The static and dynamic pull-in phenomenon of a functionally graded Al/Al₂O₃ microplate, considering the damping coefficient and fringing field effects, has been analyzed because of its crucial effect in micro-electromechanical systems application, especially in microswitches. The nonlinear equation of motion of functionally graded microplate has been derived using Hamilton’s principle, and solved analytically. Furthermore, a finite element code has been developed to solve the problem. Comparing the theoretical and numerical results for specific boundary conditions demonstrates that the numerical solution predicts the pull-in phenomenon with the least errors; and it can be used for various material power laws, damping coefficients, and initial gaps between the microplate and the substrate. The numerical results for various boundary conditions demonstrate that by increasing the damping coefficient, the dynamic pull-in voltage is also increased, and pull-in time will slow down. Moreover, the effect of power law and applied voltage on the pull-in instability is investigated.

功能梯度Al / Al ₂ O ₃的静态和动态引入现象考虑到阻尼系数和边缘场效应，对微孔板进行了分析，因为其在微机电系统应用中，特别是在微动开关中的关键作用。利用汉密尔顿原理导出了功能梯度微板的非线性运动方程，并进行了解析求解。此外，已经开发了有限元代码来解决该问题。对特定边界条件的理论和数值结果进行比较表明，数值解法可以预测引入误差最小的拉入现象。它可用于各种材料功率定律，阻尼系数以及微孔板和基材之间的初始间隙。各种边界条件的数值结果表明，通过增加阻尼系数，动态吸合电压也会增加，并且吸合时间会减慢。此外，研究了功率定律和施加的电压对吸合不稳定性的影响。