Viscous damping of perforated planar micromechanical structures.

The paper gives an analytical approximation to the viscous damping coefficient due to the motion of a gas between a pair of closely spaced fluctuating plates in which one of the plates contains a regular system of circular holes. These types of structures are important parts of many microelectromechanical devices realized in MEMS technology as microphones, microaccelerometers, resonators, etc.The pressure satisfies a Reynolds' type equation with coefficients accounting for all the important effects: compressibility of the gas, inertia and possibly slip of the gas on the plates. An analytical expression for the optimum number of circular holes which assure a minimum value of the total damping coefficient is given. This value realizes an equilibrium between the squeeze-film damping and the viscous resistance of the holes.The paper also provides analytical design formulas to be used in the case of regular circular perforated plates.