Abstract A micro-electro-mechanical (MEM) beam and column structures are analysed in details in the present work containing fixed charge ( + v e or − v e ). The transverse deflection of this column, due to the presence of fixed-charge concentration and axial compressive force, is firstly studied (linear elastic and viscoelastic cases). An analytical solution of critical buckling load P supported by MEM column, with initial imperfections due to the presence of fixed-charge in the column (simply-supported), is derived. The variation of P with fixed-charge concentration is finally obtained. A pull-in instability of MEM beam is secondly studied under the influence of external electric field, and a critical voltage V without any instability is obtained varying fixed-charge concentration inside beam. All the presented formulations are extended incorporating finite deformation (von Karman strain field) setting, as the beam rotation becomes significant at higher fixed-charge values. All the presented results are also verified with the published literature wherever it was possible. The presented work thus can be reasonably employed in the design of MEM micro-switches.

中文翻译：

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含固定电荷的微机电柱梁结构屈曲挠度研究

摘要 本文详细分析了含有固定电荷（+ ve 或- ve ）的微机电（MEM）梁柱结构。由于固定电荷集中和轴向压缩力的存在，该柱的横向挠度首先被研究（线弹性和粘弹性情况）。推导出了由 MEM 柱支撑的临界屈曲载荷 P 的解析解，由于柱中存在固定电荷（单支撑）而存在初始缺陷。最终得到 P 随固定电荷浓度的变化。其次研究了在外电场影响下MEM束的引入不稳定性，并获得了无任何不稳定的临界电压V，改变束内的固定电荷浓度。所有提出的公式都扩展了结合有限变形（von Karman 应变场）设置，因为束旋转在更高的固定电荷值下变得显着。所有呈现的结果也尽可能通过已发表的文献进行验证。因此，所提出的工作可以合理地用于 MEM 微开关的设计。