Squeeze-film damping of flexible microcantilevers at low ambient pressures: theory and experiment

An improved theoretical approach is proposed to predict the dynamic behavior of long, slender and flexible microcantilevers affected by squeeze-film damping at low ambient pressures. Our approach extends recent continuum gas damping models (Veijola 2004 J. Micromech. Microeng. 14 1109–18, Gallis and Torczynski 2004 J. Microelectromech. Syst. 13 653–9), which were originally derived for a rigid oscillating plate near a wall, to flexible microcantilevers for calculating and predicting squeeze-film damping ratios of higher order bending modes at reduced ambient pressures. Theoretical frequency response functions are derived for a flexible microcantilever beam excited both inertially and via external forcing. Experiments performed carefully at controlled gas pressures are used to validate our theoretical approach over five orders of the Knudsen number. In addition, we investigate the relative importance of theoretical assumptions made in the Reynolds-equation-based approach for flexible microelectromechanical systems. (Some figures in this article are in colour only in the electronic version)