  In this work, we employ a kinetic theory based approach to predict the
hydrodynamic forces on electromechanical resonators operating in gaseous media.
  Using the Boltzmann-BGK equation, we investigate the influence of the
resonator geometry on the fluid resistance in the entire range of
nondimensional frequency variation $0\le\tau\omega\le\infty$; here the fluid
relaxation time $\tau=\mu/p$ is determined by the gas viscosity $\mu$ and
pressure $p$ at thermodynamic equilibrium, and $\omega$ is the (angular)
oscillation frequency. Our results support the experimentally observed
transition from viscous to viscoelastic flow in simple gases at
$\tau\omega\approx1$. They are also in remarkable agreement with the measured
geometric effects in resonators in a broad linear dimension, frequency, and
pressure range.
