中文摘要：

基于应变梯度理论，建立静电力驱动微梁的控制方程，通过瑞利．利兹法对微梁的控制方程进行降阶，得到一组非线性代数方程。利用牛顿一拉菲森法求解该方程组，确定微梁的吸合电压，分析应变梯度对吸合电压的影响规律。结果表明，当微梁的无量纲厚度减小时，无量纲吸合电压将显著增大，表现出明显的尺寸效应；随着材料内禀特征长度的增加，无量纲吸合电压的尺寸效应也越显著，说明应变梯度对微梁的吸合电压影响显著。随着微梁无量纲厚度的减小，残余应力对无量纲吸合电压影响显著，可以减弱应变梯度对无量纲吸合电压的影响；同时应变梯度可以显著降低中面伸长对吸合电压的影响。分析结果可为微机电系统中微梁的设计提供参考。

英文摘要：

The governing equation of the micro-beam actuated by electrostatic force was derived based on the strain gradient theory with the aid of variational principle. The reduce model was obtained based on the Rayleigh-Ritz method. The pull-in voltage was solved by the Newton-Raphson method. Effects of the strain gradient on the pull-in voltage were investigated. The results show that the dimensionless pull-in voltage increases significantly with the dimensionless micro-beam thickness decreasing, showing a significant size effect. When the intrinsic material characteristic length increases, the size effect of the dimensionless pull-in voltage is more significantly, indicating that the effect of the strain gradient on the micro-beam pull-in voltage is remarkable. When the dimensionless micro-beam thickness decreases, the effect of the residual stress on the dimensionless pull- in voltage is significant. The size effect of the normalized pull-in voltage is weakened when the residual stress increases, indicating the residual stress can decrease the effect of the strain gradient on the pull-in voltage. The effect of the mid-plane stretch on the pull-in voltage is reduced markedly when the strain gradient is considered. The results can prove the reference in the design of micro structures in MEMS （micro-electrical-mechanical system）.