Squeeze-film damping characteristics of cantilever microresonators for higher modes of flexural vibration

Abstract

Squeeze-film characteristics of electrostatically actuated microcantilevers observed under large DC load coupled with small AC component are presented for the first three flexural modes of vibration of the resonator operating in different ambient pressure conditions. A semi-analytical model of an electrostatically actuated microcantilever beam is developed taking into account the dependency of the effective viscosity on variable gap spacing through the variable Knudsen number. The quality factors of the system are also obtained numerically using the coupled field FE analysis software ANSYS. A comparison of the results up to the pull-in instability shows excellent agreement for damping characteristics obtained by both the semi-analytical and FE methods. The effects of large DC bias voltages on quality factor and resonance frequency are found to differ considerably for the different flexural modes of vibration of the resonator. Under rarefied flow conditions, variations in ambient pressure significantly influence the squeeze film damping characteristics for the entire range of DC polarization. A comparison between compressible and incompressible flow models predicts notable difference in the squeeze-film characteristics.

Keywords: MEMS, Electrostatic actuation, Squeeze-film damping, Rarefied flow, Resonant sensor.