INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF MICROMECHANICS AND MICROENGINEERING J. Micromech. Microeng. 15 (2005) 2083–2092 doi:10.1088/0960-1317/15/11/013 Analytical solutions for the stiffness and damping coefficients of squeeze films in MEMS devices with perforated back plates S S Mohite 1 , Haneesh Kesari 2 , V R Sonti 1 and Rudra Pratap 1 1 CranesSci MEMS Lab, Department of Mechanical Engineering, Indian Institute of Science, Bangalore-560 012, India 2 Department of Mechanical Engineering, Indian Institute of Technology, Guwahati-781 039, Assam, India E-mail: pratap@mecheng.iisc.ernet.in Received 7 February 2005, in final form 26 August 2005 Published 23 September 2005 Online at stacks.iop.org/JMM/15/2083 Abstract Closed-form expressions for the stiffness and the damping coefficients of a squeeze film are derived for MEMS devices with perforated back plates. Two kinds of perforation configurations are considered—staggered and matrix or non-staggered configuration. The analytical solutions are motivated from the observation of repetitive pressure patterns obtained from numerical (FEM) solutions of the compressible Reynolds equation for the two configurations using ANSYS. A single pressure pattern is isolated and further subdivided into circular pressure cells. Circular geometry is used based on observed symmetry. Using suitable boundary conditions, the Reynolds equation is analytically solved over the pressure cells. The complex pressure obtained is used to identify the stiffness and damping offered by the pressure cells. The stiffness and damping forces due to pressure cells within a pattern are added up separately. In turn, the stiffness and damping due to all the patterns are summed up resulting in the stiffness and damping forces due to the entire squeeze film. The damping and spring forces thus obtained analytically are compared with those obtained from the FEM simulations in ANSYS. The match is found to be very good. The regime of validity and limitations of the analytical solutions are assessed in terms of design parameters such as pitch to air gap, hole length to diameter and pitch to hole radius ratios. The analysis neglects inertial effects. Hence, the results are presented for low values of Reynolds number. 1. Introduction 1.1. Literature review The dynamics of MEMS devices involves air–structure interactions to varying degrees. Some devices, such as accelerometers, gyroscopes and RF switches, etc, can be designed to work in rarified atmosphere, whereas some devices, such as microphones, ultrasonic transducers and micro mirrors, etc, generally work with ambient air surrounding them. It is well known that the thin layer of air between the planar structures having relative motion can significantly alter the dynamic characteristics of these devices by adding stiffness and damping to the system. The dynamic response of these devices can be studied efficiently by modelling as equivalent circuits with lumped parameters [1, 2]. For this modelling, however, an accurate estimate of the stiffness and the damping offered by the air film is essential in addition to the several other system parameters that can be obtained from known formulae. The central motivation of this study is to provide closed-form expressions for estimating 0960-1317/05/112083+10$30.00 © 2005 IOP Publishing Ltd Printed in the UK 2083