求解力电耦合方程的控制弧长法

The arc-length method for solving the coupled equation of mechanics-electricity

静电作用下的柔性薄板是微电机械的核心部件,其控制方程是变形控制方程和静电平衡方程构成的一组非线性耦合方程。本文在分别给出求解这两组方程数值方法的基础上,把控制弧长法进行了合理的推广,变直接加载电压为由构型控制的电压加载方式。结果表明这种方法不仅能够克服收敛性难的问题,而且能够得到致动板吸入失稳后的构形。算例还表明用本方法计算的吸入临界值要比用解析模型得到的临界值更接近实验值。

Flexible plate subjected to static electric force is a key component of MEMS. And its governing equation is a group of nonlinear coupled equation consisted of static equilibrium equation and static electric equilibrium equation. On the based of giving the means of solving these equations, that the arclength method is generalized result in loading pattern change that turn directly loading voltage into indirectly loading voltage by deflection control. It is shown that the method not has the excellent convergence but be able to give the deformation after pull-in. Numerical examples show that pull-in threshold calculated by this method is more agreement with experiment value than analytical model.