尺度依赖的静电驱动各向异性微板的Pull-in效应

Size dependent Pull-in effect of electrostatically actuated anisotropic micro-plates

在新修正偶应力理论的基础上建立了一种可用于分析静电驱动各向异性微板的尺度依赖模型。模型中包含有两个材料尺度参数,在考虑材料宏观各向异性的同时也考虑了微观各向异性程度对结构Pull-in特性的影响。通过虚功原理推导了静电驱动微板的非线性控制方程并显式地给出了Pull-in电压和挠度的表达式。算例结果表明:本文模型所预测的Pull-in电压和挠度分别大于和小于经典宏观板理论的预测结果,即反映了微尺度结构下的尺度效应。尺度效应的影响在板厚度与材料尺度参数接近时逐渐增加,而随着两者比值的增加,该影响逐渐减弱,最终可以忽略不计。此外,本文也讨论了初始间隙d对Pull-in电压以及尺度效应的影响。结果表明随着d的增加,Pull-in电压随之增大,而Pull-in挠度变化不大。

In this paper,a size dependent model of electrostatically actuated anisotropic micro-plate is proposed based on a modified couple stress theory.This model contains two material size parameters so as to simultaneously take into account macroscopic and microscopic anisotropy on the structural Pull-in characteristic.The governing equations are derived using virtual work principle and solved by utilizing a reduced-order model.The explicit expressions of Pull-in voltage and transverse deflection are given.Numerical results demonstrate that the Pull-in voltage and bending deflection predicted by this model are respectively larger and smaller than classical macroscopic plate theory,i.e.the size effect can be well depicted.The influences of size effect are most noticeable when the ratio of plate thickness to material size parameter approaches to 1,and the size effect would be gradually weak and neglectable if the ratio increases.In addition,the effects of initial gap on Pull-in voltage and size effect are also discussed.