Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 959232, 6 pages http://dx.doi.org/10.1155/2013/959232 Research Article Modeling the Electrostatic Deflection of a MEMS Multilayers Based Actuator Hassen M. Ouakad, Mohammad A. Hawwa, and Hussain M. Al-Qahtani Department of Mechanical Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia Correspondence should be addressed to Hassen M. Ouakad; houakad@kfupm.edu.sa Received 2 July 2013; Revised 26 October 2013; Accepted 1 November 2013 Academic Editor: Wei-Chiang Hong Copyright © 2013 Hassen M. Ouakad et al. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. An actuator comprised of a rigid substrate and two parallel clamped-clamped microbeams is modeled under the inluence of electrostatic loading. he problem is considered under the context of nonlinear Euler’s mechanics, where the actuating system is described by coupled integrodiferential equations with relevant boundary conditions. Galerkin-based discretization is utilized to obtain a reduced-order model, which is solved numerically. Actuators with diferent gap sizes between electrode and beams are investigated. he obtained results are compared to simulations gotten by the inite-element commercial sotware ANSYS. 1. Introduction One of the basic and most common MEMS devices is the parallel-plate electrostatic actuator. A clear advantage of the parallel-plate electrostatic actuators is their capability of generating high force. One drawback of these actuators, however, is the low delection they can perform due to the gap size between the parallel plates and the induced pull-in instability caused by system nonlinearities. he main source of these nonlinearities is the fact that the electrostatic produced force is inversely proportional to the squared value of the gap distance between the two electrodes. Inclusive analyses of the pull-in instability can be found in published papers by Gupta et al. [1], Nielson and Barbastathis [2], Nayfeh et al. [3], and Khater et al. [4]. In order to put limitations on the instability domain, an intuitive solution is to decrease the gap distance between the parallel plates. Two additional actions can also help: (i) reduction of the rigidity of the parallel plates and (ii) increase the areas of the electrostatic surfaces. here have been several attempts to increase the stable range of travel of parallel-plate actuators. Early attempts include the use of curved electrodes [5], utilizing leveraged bending and strain stifening [6], and employing feedback control algorithms to increase dynamic range [7]. A unique approach of intensifying the electrostatic force and increasing the out-of-plane delection was to utilize more than one parallel-plate electrostatic device built in parallel fashion. Abbaspour-Sani and Afrang [8] proposed a structure composed of two displaceable microplates for a microswitch application. Chafey and Austin [9] pre- sented another microswitch made of a double-cantilever microbeam structure. Samaali et al. [10] demonstrated a double-cantilever microbeam to design an RF microswitch. In all of these attempts, researchers were able to reduce pull- in voltages, switching time and power consumption. Inspired by these works, the current work is intended to provide an analytical solution for the delection of a parallel double actuator comprised of a ixed electrostatic substrate and two electrostatic parallel layers. A continuum model based on Euler’s beam is used to describe the two clamped- clamped parallel microbeams under the inluence of applied voltage. he presented model includes the efect of geometric nonlinearity due to midplane stretching. he quasi-static response of a single actuator (made of a substrate and a single electrostatic layer) is compared with that of double actuators (made of a substrate and two electrostatic layers). hen, a inite-element numerical solution is obtained by utilizing ANSYS, and a comparison between both solutions is presented.