Viscous energy dissipation in laterally oscillating planar microstructures: a theoretical and experimental study

The authors investigate energy loss in an incompressible, viscous fluid layer that provides skin-friction damping for a laterally oscillating planar microstructure. The physical model for the viscous dissipation is based on Stokes-type fluid motion. In the theoretical analysis, the damping property of a fluid layer is characterized in terms of viscous energy dissipation, resulting in damping formulas for practical Q estimation. In the experimental study, surface-micromachined polysilicon resonators have been fabricated and tested under an electrostatic excitation in atmosphere. The estimated Q compares well with the Q measured for the test structures, as well as with the experimental Q reported by previous investigators. It is concluded that the Stokes-type damping model presents a more general damping treatment with better Q estimation, although discrepancies of 10 to 20% still remain between the estimated and measured Q. Possible sources of these discrepancies are discussed. The results of the study are applicable to damping design for microsensors and microactuators