INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF MICROMECHANICS AND MICROENGINEERING J. Micromech. Microeng. 14 (2004) 1302–1306 PII: S0960-1317(04)74185-6 Characterization of the squeeze film damping effect on the quality factor of a microbeam resonator C Zhang, G Xu and Q Jiang Department of Mechanical Engineering, University of California at Riverside, CA 92521, USA E-mail: gxu@engr.ucr.edu Received 2 January 2004, in final form 11 May 2004 Published 13 July 2004 Online at stacks.iop.org/JMM/14/1302 doi:10.1088/0960-1317/14/10/003 Abstract The squeeze film damping effect on a beam resonator is analyzed on the basis of the coupled elastic beam theory and the Reynolds equation for isothermal incompressible gas films. Under the condition of small amplitude oscillation, linearization of the governing equations leads to the solution that characterizes the squeeze film damping effect on the beam resonator by two dimensionless parameters. These two parameters, in analogy with the damping and mass parameters of the simple mass-spring-damping system, are completely determined by the physical properties of the beam and gas. It is shown that the calculation of these two parameters can be considerably simplified according to the value of the squeeze number. 1. Introduction Small vibrational structures, typically in the shape of beam and plate at the micron scale fabricated by silicon technology, have received ever increasing interest because they can be used as key components in developing sophisticated microelectromechanical systems (MEMS) including micro- sensors and actuators [1–4]. One of the important issues involved in these developments is to characterize the interaction of the vibrational structure with the thin layer gas between the structure and its supporting substrate [5–7]. This interaction, termed the squeeze film damping effect, is governed by coupled solid deformation and fluid flow equations (e.g. [8]). The squeeze film damping effect on the dynamics of microstructures has been extensively studied [5–9]. These analyses employ the Reynolds equation for isothermal incompressible gas films to describe the characteristics of the squeeze film. The microstructure, however, is generally assumed to be rigid, simplifying the coupled solid–fluid field problem as a one degree spring-mass-damper problem. This assumption also decouples the Reynolds equation, which leads to analytical solutions when the linearization is applied under a condition of small amplitude oscillation. On the other hand, one may study the squeeze film damping effect using the numerical approach such as the finite element method to directly solve the coupled solid deformation and fluid flow equations. Such an approach, though widely employed in other field such as blood flow in veins, may appear to be somewhat inconvenient for designing MEMS microstructures because of the difficulties to sort out the non-linear effects of many physical parameters from demanding computational efforts, even for the reduced- order models that have been developed to reduce the simulation time at the expense of computational accuracy [7]. In this paper, we present a first-order analysis of the squeeze film damping effect based on the coupled elastic beam theory [10] and the Reynolds equation for incompressible fluid films [11, 12]. The beam is assumed to be under small amplitude oscillation. The Reynolds equation is then linearized by the perturbation method. The solution of the coupled solid deformation and fluid flow equations shows that the squeeze film damping effect on the beam resonator can be characterized by two dimensionless parameters, in analogy with the damping and mass parameters in the simple mass- spring-damping system. These two parameters, determined by the physical properties of the beam and gas in the form 0960-1317/04/101302+05$30.00 © 2004 IOP Publishing Ltd Printed in the UK 1302