Authors: T. Veijola
Affilation: Helsinki University of Technology, Finland
Pages: 162 - 165
Keywords: gas damping, effective viscosity, Knudsen number, rarefied Couette flow, damping in microstructures
Compact models for the viscous damping coefficient in narrow air gaps between laterally moving structures are reported. The gas rarefaction effects are included in these small-displacement models. In the first part of the paper, a simple frequency-independent first-order slip- ow approximation for the damping coefficient is derived. The resulting simple approximation has a maximum relative error of less than 0:6 % at arbitrary Knudsen numbers at viscous, transitional and free molecular regions. In the second part of the paper, the dynamic model for the damping force is derived, considering again the gas rarefaction, by applying the slip-velocity boundary conditions. An analytic expression for the damping coefficient to be used in the frequency-domain analysis of an oscillating structure is presented. These dynamic model is implemented also as an electrical equivalent admittance, constructed of RC sections, to allow both frequency and time domain simulations with a circuit simulator.
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