Presented in this study is an analytical investigation on the size-dependent nonlinear vibration and pull-in instability of circular microplates subjected to the electrostatic, Casimir, and hydrostatic forces. Based on the modified strain gradient theory in conjunction with the Kirchhoff thin plate theory and von Kármán’s nonlinear kinematic relations, the governing equations were derived using the variational principle. The Galerkin technique (GT) and Homotopy analysis method (HAM) are employed to present the analytical solution considering the clamped boundary condition. Different comparative studies are presented to show the accuracy of the model. As the main novelty of this study, the effects of the geometric nonlinearity on the strain gradient dynamic pull-in instability of circular microplates are presented through a wide range of analytical results. It is observed that by increasing the gap distance, the impacts of nonlinear strains on pull-in behavior become more remarka...

中文翻译：

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基于修正应变梯度理论的几何非线性对圆形微板拉入不稳定性的影响

本研究提出的是对圆形微孔板在静电，卡西米尔和静水压力作用下，尺寸相关的非线性振动和拉入不稳定性的分析研究。基于修正的应变梯度理论，结合基尔霍夫薄板理论和冯·卡尔曼的非线性运动学关系，利用变分原理推导了控制方程。考虑约束边界条件，采用Galerkin技术（GT）和同伦分析方法（HAM）给出了解析解。提出了不同的比较研究以显示模型的准确性。作为这项研究的主要新颖之处，通过广泛的分析结果，提出了几何非线性对圆形微板应变梯度动态拉入不稳定性的影响。观察到，通过增加间隙距离，非线性应变对拉入行为的影响变得更加明显。