Numerical and analytical modelling of trapped gas in micromechanical squeeze-film dampers

Damping in air gaps of micromechanical devices that vibrate out-of-plane is studied at frequencies where the acoustic wavelength is comparable with the air gap dimensions. A FEM study with a viscoacoustic solver shows that above a certain frequency, closed damper borders can be assumed in the approximate analysis of the squeeze-film damper, regardless of the practical border conditions. Here, this closed-border (trapped gas) problem is solved analytically from the linearized Navier–Stokes equations in 1D. This results in a compact model for the mechanical impedance that accounts for damping, inertial and spring forces as well as thermal behaviour and slip border conditions. The model produces the gas resonances in the air gap when the wavelength of the acoustic wave is smaller than the gap dimensions. Due to the slip conditions, the model is valid in modeling micromechanical oscillating structures with small air gaps.