On the calculation of viscous damping of microbeam resonators in air

Theoretical aspects concerning the calculation of the air damping of microbeam resonators in the framework of continuum fluid mechanics are discussed. A closed relationship between Knudsen and Stokes numbers is derived, which indicates that the no-slip flow regime is attained in systems that operate at high Stokes numbers only, while systems that operate at low Stokes numbers invariably enter the slip flow regime. These observations are relevant to improve the modelling and simulation of microbeam resonators integrated to micro-electromechanical systems (MEMS). In addition, analytical expressions of the viscous damping coefficients for different flow regimes are discussed in relation to experimental data.