1 Abstract—Pull-in instability is a nonlinear and crucial effect that is important for the design of microelectromechanical system devices. In this paper, the appropriate electrostatic voltage range is determined by measuring fluid flow pressure via micro pressure sensor based microbeam. The microbeam deflection contains two parts, the static and perturbation deflection of static. The second order equation regarding the equivalent stiffness, mass and damping matrices based on Galerkin method is introduced to predict pull-in instability due to the external voltage. Also the reduced order method is used for solving the second order nonlinear equation of motion. Furthermore, in the present study, the micro capacitive pressure sensor is designed for measuring special fluid flow pressure range. The results show that the measurable pressure range can be optimized, regarding damping field and external voltage. Keywords—MEMS, pull-in instability, electrostatically actuated microbeam, reduced order method. I. INTRODUCTION ICROELECTROMECHANICAL system (MEMS) devices have been widely used in extensive aerospace applications, information technology, and biomaterials. The small size, light weight, and low cost production have been the reason which makes commercialization attractive. These de- vices are an integration of actuators, mechanical elements, sensors, and electronics [1], [2]. Microbeams have been extensively used in MEMS applications over past decades. Indeed, simple configuration, low energy consumption and appropriate compatibility of electrically actuated microbeam devices have attracted researchers’attentions. The actuated microbeam model consists of an elastic beam suspended over a ground plate, and dielecteric fills the gap between them [3]. While the voltage exceeds a critical point, the elastic beam deflects and collapses. This phenomenon is a crucial point in MEMS designing and known as pull-in instability [4], [5], [7]. The static displacement and stress of clamped – clamped beam under various loadings based on shooting model was investigated by Choi and Lovel [6]. They promoted size dependent microbeam model for predicting the pull-in. Zhang and Zhao [5] have introduced a numerical and analytical method for studying pull-in instability of microstructures under electrostatic force. They developed a one-mode approach based on Galerkin reduced order method gathering with Cardan’s solution of cubic equation. Recently, the Yashar Haghighatfar is with the Mechanical Engineering, AmirKabir University of Technology, Tehran, Iran (corresponding author, e-mail: y.haghighatfar@aut.ac.ir). Shahrzad Mirhosseini is with the Mechanical Engineering, AmirKabir University of Technology, Tehran, Iran. utilization of microbeams coupled with fluid flow in MEMS devices has been reported for measuring pressure. In this case, the investigators show their interest in micro-fluid devices such as micropump, biomedical, and biological MEMS applications [8]-[10]. Puers and Baert [11] performed voltage analysis of electrostatically actuated beam structures with fixed–fixed and fixed–free end conditions. They presented closed form solution for the pull-in voltage based on lumped spring–mass system. Sadeghian [12] examined the application of the generalized differential quadrature method to the study of pull-in. Ho and Tai [13] opened up a new territory for flow control with MEMS. Although, there are many researches working on dynamics of microbeams containing internal flow without electrostatic field, the dynamic and pull-in instability of microbeam conveying fluid flow is limited. In this article, a theoretical model is applied to predict dynamic and pull-in instability for measuring fluid pressure. In the proposed model, the influence of nonlinear electrostatic force [14], microstructure and damping field is considered in MEMS devices to optimize the design for measuring special ranges of harmonic pressure. II. MATERIALS AND METHODS The governing equations using Euler-Bernoulli beam theory with damping effects, are written as follows 4 2 ( ,) (,) (,) (,) 4 2 xt xt xt x t y y y EI s c f x t t           (1) Based on Galerkin method, beam equation is discretized in order to compute equivalent stiffness, mass and damping (,) 1 ( ). () n xt i i i y x t      (2) in which the shape function satisfies boundary conditions and determines the time participation coefficient of each mode shape. Substituting (2) in (1) leads to 4 2 1 1 4 2 1 ( ). () ( ). () ( ). () Re n n i i i i i i n i i i x t x t EI s x t x t c t                       (3) Pull-In Instability Determination of Microcapacitive Sensor for Measuring Special Range of Pressure Yashar Haghighatfar, Shahrzad Mirhosseini M World Academy of Science, Engineering and Technology International Journal of Mechanical and Mechatronics Engineering Vol:12, No:6, 2018 653 International Scholarly and Scientific Research & Innovation 12(6) 2018 scholar.waset.org/1307-6892/10009170 International Science Index, Mechanical and Mechatronics Engineering Vol:12, No:6, 2018 waset.org/Publication/10009170