Higher order correction of electrostatic pressure and its influence on the pull-in behavior of microstructures

In close gap electrostatic microactuators modeling, distributed forces are commonly approximated using a parallel capacitor formula, adequate when the distance between electrodes is much smaller than their length. In the present work, using the perturbation theory, we develop simple expressions for electrostatic pressure with higher order corrections, mainly related to the curvature and slope of the electrode. These approximate expressions are validated through a comparison with analytical solutions for simple geometries as well as numerical results. The influence of the higher order correction on the pull-in behavior is illustrated for a large deflection model of a one-dimensional membrane (string), subjected to electrostatic and uniform mechanical pressure. An analytical solution is built and compared with the numerical solution obtained by the collocation method. The initial curvature of the string has a strong influence on the pull-in behavior. In the case of the nonlinear deflection-dependent tensile force, string bistability is possible.