Squeeze-film damping of circular microplates vibrating in a tilting motion

Accurate determination of squeeze-film damping (SFD) plays an important role in the design of high-Q microresonators. Many analytical models for predicting SFD on the microplate vibrating in a tilting motion have been well established in the past. However, most of the previous works focused on the rectangular torsion microplates. There are few analytical models for the SFD on the circular microplate vibrating in the tilting motion. Only one model was developed by Xia et al. (Microfluid Nanofluid 19:585–593, 2015). However, the gas in the air gap was treated as an incompressible gas in their model, and the perforation effect was not considered. This paper first studies the SFD on a non-perforated circular microplate vibrating in the tilting motion. The effects of both gas compressibility and rarefaction are considered in a modified Reynolds equation. The air pressure under the circular microplate is approximated by using Bessel series. A more accurate analytical expression for the damping and spring constants has been developed. Then, the model for the non-perforated microplates is extended to include the perforation effect. The present models are validated by comparison of the numerical results obtained by finite element method over a wide range of frequency and perforation ratios.