Structural Behavior of Microbeams Actuated by Out-of-Plane Electrostatic Fringing-Fields

In this paper, we present an investigation of the static behavior of a doubly-clamped microbeam actuated electrically through out-of-plane electrostatic fringing-fields. The distributed electrostatic force is caused by the asymmetry of the fringing-fields. This is actually due to the out-of-plane asymmetry of the beam and its two actuating stationary electrodes. The electric force was approximated by means of fitting the results of two-dimensional numerical solution of the electrostatic problem using Finite-Element Method (FEM). Then, a reduced-order model (ROM) was built using the Galerkin decomposition with linear undamped modes of a clamped-clamped beam as base functions. The ROM equations are solved numerically to get the static response of the considered micro-actuator when actuated by a DC load. Results shows possibility of having three different regimes for this particular MEMS device: a bending regime, a catenary regime, and an elastic regime. Eigenvalue problem is then solved to get the variation of the fundamental natural frequency when the system is deflected by a DC load. 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 a pull-in scenario.