Characterization of the squeeze film damping effect on the quality factor of a microbeam resonator

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.