静电激励MEMS微结构吸合电压尺寸效应研究

基于应变梯度弹性理论，研究了静电激励MEMS微结构吸合电压的尺寸效应。利用最小势能原理分别推导出含尺寸效应的一维梁模型和二维板模型的高阶控制方程。采用广义微分求积法和拟弧长算法对控制方程进行了数值求解。结果表明，随着结构尺寸的降低，新模型所预测的归一化的吸合电压呈非线性增长，表现出尺寸效应 (特别是当结构尺寸与内禀常数在同一数量级时尺寸效应更加强烈)；而相应的经典理论模型并不能预测此尺寸效应。两种新模型可视为相应经典理论的推广。论文有助于研究MEMS微结构的特性并对微结构的设计有潜在的应用价值。

The size-dependent pull-in voltage of electrostatically actuated MEMS is studied using strain gradient elasticity. The microbeam model and microplate model are derived respectively via the principle of minimum potential energy. The generalized differential quadrature method and pseudo arclength algorithm are used to solve the high-order PDEs. It is shown that the normalized pull-in voltage predicted by the new models increases nonlinearly with the decrease of the structure thickness, exhibiting size effect (and the size effect is particularly strong when the structural thickness is on the same order of the characteristic material length scale parameter); while the corresponding classical models do not exhibit such a size effect. The two new models may be regarded as extensions of the corresponding classical ones. This study may be helpful to characterize the mechanical properties of small sized MEMS, or guide the design of microstructures for a wide range of potential applications.