Static response and natural frequencies of microbeams actuated by out-of-plane electrostatic fringing-fields

In this paper, we investigate the static behavior of a doubly-clamped microbeam actuated electrically through out-of-plane electrostatic fringing-fields. The resultant actuation force is caused by the asymmetry of the electric fringing-fields. This is designed due to the out-of-plane asymmetry of the beam and its two actuating stationary electrodes. The electric force was estimated by means of fitting the results of the two-dimensional numerical solution of the electrostatic problem using Finite-Element Method (FEM). Then, a reduced-order model (ROM) was derived using the Galerkin decomposition with mode-shapes of a clamped-clamped beam as basis functions. The ROM equations are solved numerically to get the static response of the considered micro-actuator when actuated by a DC load. The results show the possibility of having three different regimes for this particular MEMS device: a bending regime, a catenary regime, and an elastic regime. The eigenvalue problem is then derived and examined to get the variation of the fundamental as well as higher-order natural frequencies when the system is deflected by a DC load. The results show that controlling the microbeam stroke, with a DC voltage on the gate electrodes, enables us to tune the system frequency, resulting in a possibility of a tunable MEMS device without any pull-in scenario.