Viscous microstructural dampers with aligned holes: design procedure including the edge correction.

The paper is a continuation of the works "Modelling of viscous damping of perforated planar micromechanical structures. Applications in acoustics" [Homentcovschi and Miles, J. Acoust. Soc. Am. 116, 2939-2947 (2004)] and "Viscous Damping of Perforated Planar Micromechanical Structures" [Homentcovschi and Miles, Sensors Actuators, A119, 544-552 (2005)] where design formulas for the case of an offset (staggered) system of holes was provided. The present work contains design formulas for perforated planar microstructures used in MEMS devices (such as proof-masses in accelerometers, backplates in microphones, micromechanical switches, resonators, tunable microoptical interferometers, etc.) in the case of aligned (nonstaggered) holes of circular and square section. The given formulas assure a minimum total damping coefficient (including the squeeze film damping and the direct and indirect resistance of the holes) for an assigned open area. The paper also gives a simple edge correction, making it possible to consider real (finite) perforated planar microstructures. The proposed edge correction is validated by comparison with the results obtained by FEM simulations: the relative error is found to be smaller than 0.04%. By putting together the design formulas with the edge correction a simple integrated design procedure for obtaining viscous perforated dampers with assigned properties is obtained.