Abstract

This paper investigates the instability and buckling characteristics of a porous microplate under the influence of electrostatic fields, taking into account the implications of the intermolecular Casimir forces. Employing the modified couple stress theory, this research formulates equations that encapsulate the interplay between electrostatic and Casimir forces within porous plates. The analysis integrates distributed support loads, employing both Galerkin mode summation and finite element methods to solve static deformation equations and determine pull-in instability voltages and buckling loads. A novel approach is introduced, and equilibrium relationships are derived with respect to displacement to determine both the buckling load and instability voltage. This study effectively compares classical and non-classical theories, scrutinizing the effects of dimensionless length scale parameters and porosity ratios on maximum displacement, pull-in instability voltages, and buckling loads. The results demonstrate that the analytical method converges swiftly and aligns with the findings of the finite element method. The method for deriving equilibrium relationships proves to be accurate in predicting both instability voltage and buckling load. Additionally, the instability voltage exhibits an almost linear relationship with variations in the percentage of porosity, and similarly, the buckling load undergoes linear changes with alterations in porosity percentage. Hence, formulas for the linear relationships are calculated for both of these associations.

中文翻译：

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静电场和卡西米尔力下多孔微板的尺寸依赖性屈曲和不稳定性

摘要

本文研究了多孔微板在静电场影响下的不稳定性和屈曲特性，并考虑了分子间卡西米尔力的影响。本研究采用修正的力偶应力理论，制定了封装多孔板内静电力和卡西米尔力之间相互作用的方程。该分析集成了分布式支撑载荷，采用伽辽金模式求和和有限元方法来求解静态变形方程并确定拉入失稳电压和屈曲载荷。引入了一种新颖的方法，并导出了关于位移的平衡关系，以确定屈曲载荷和不稳定电压。这项研究有效地比较了经典和非经典理论，仔细研究了无量纲长度尺度参数和孔隙率对最大位移、拉入不稳定电压和屈曲载荷的影响。结果表明，该分析方法收敛速度很快，并且与有限元方法的结果一致。事实证明，推导平衡关系的方法可以准确地预测不稳定电压和屈曲载荷。此外，不稳定电压与孔隙率百分比的变化几乎呈线性关系，并且类似地，屈曲载荷随着孔隙率百分比的变化而经历线性变化。因此，针对这两种关联计算线性关系的公式。