考虑卡西米尔力的静电激励NEMS吸合特性及其尺寸效应研究

基于应变梯度理论和哈密顿原理，并考虑卡西米尔力的影响，建立了静电激励纳米机电系统(NEMS)的尺寸效应模型，并得到模型的控制方程和边界条件。然后，引入广义微分求积法和拟弧长算法，得到模型的数值解。结果表明，当考虑卡西米尔力的影响时，系统两极的吸合电压有所减小。并且，当系统尺寸达到一个临界值时(即两电极间距小于“最小间距”，或可变形电极长度超过“拉起长度”)，系统会在没有外加电压的作用下自动发生吸合，这将为NEMS的优化设计和定量分析提供理论基础。

Study on Size Dependence and Pull-in Instability of Electrostatically Actuated NEMS with Casimir Force

Based on the strain gradient elasticity theory and Hamilton principle, a size-dependent model including Casimir force for the electrostatically actuated Nano-Electro-Mechanical Systems(NEMS) is presented, and the governing equation and boundary conditions are derived. The problem is solved numerically with the help of generalized differential quadrature method and pesudo-arclength algorithm. The results reveal that Casimir force can reduce the pull-in voltage of system. And once scale of system reach to the critical value (the gap between two electrodes is less than minimum gap, or the length of movable beam is larger than the detachment length), the pull-in instability would occur without voltage applied. The study may be helpful for the design and theoretical modeling of NEMS incorporating Casimir force.