A numerical study of squeeze-film damping in MEMS-based structures including rarefaction effects

摘要

In a variety of MEMS applications, the thin film of fluid responsible of squeeze-film dampingresults to be rarefied and, thus, not suitable to be modeled though the classical Navier-Stokes equation. Thesimplest way to consider fluid rarefaction is the introduction of a slight modification into its ordinaryformulation, by substituting the standard fluid viscosity with an effective viscosity term. In the present paper,some squeeze-film damping problems of both parallel and torsion plates at decreasing pressure are studied bynumerical solving a full 3D Navier-Stokes equation, where the effective viscosity is computed according toproper expressions already included in the literature. Furthermore, the same expressions for the effectiveviscosity are implemented within known analytical models, still derived from the Navier-Stokes equation. In allthe considered cases, the numerical results are shown to be very promising, providing comparable or evenbetter agreement with the experimental data than the corresponding analytical results, even at low air pressure.Thus, unlike what is usually agreed in the literature, the effective viscosity approach can be efficiently applied atlow pressure regimes, especially when this is combined with a finite element analysis (FEA