Novel Reduced Order Model for Electrically Actuated Microbeam-Based MEMS

We present a novel semi-analytical approach to solve nonlinear integral-partial-differential equation related to MEMS microactuators. The proposed approach is based on a reduced-order model of microbeams under the action of electrostatic force. Using Euler-Bernoulli beam theory, we derive the nonlinear equations governing the motion of a doubly clamped microbeam. The formulated model gives good account of nonlinearities such as midplane stretching effects and nonlinear electrostatic force. The dynamic response of the coupled electro-mechanical microsystem is simulated through an innovative approach based on a Galerkin procedure, which allows the use of only one mode in the ROM decomposition. Basis function of the Galerkin decomposition is obtained through the DQM decomposition. The obtained ROM is utilized in combination with the Finite Difference Method to simulate the limit cycle solutions of the microactuator. The novel ROM is applied to study cases provided in the literature and compared with classical Galerkin technique.