Modified Reynolds' equation and analytical analysis of squeeze-film air damping of perforated structures

We modified the Reynolds equation to extend its applications to squeeze-film air damping of perforated plates (i.e., the hole-plates) by adding a term related to the damping effect of gas flow through holes. The modified Reynolds equation (MRE) is generally effective for a perforated hole-plate with a finite thickness and finite lateral dimensions as well as a non-perforated hole-plate. Analytical expressions of damping pressure for long rectangular hole-plates and regular rectangular hole-plates have been found. For MEMS devices with typical dimensions, 'effective damping width' approximation is introduced so that the boundary effect on damping force can be treated easily. The conditions for 'effective damping width' approximation are discussed. Based on the concept of 'effective damping width', damping forces for circular plates and even hole-plates with irregular shapes can be found. The results obtained by the MIZE method match the numerical results obtained by ANSYS/FLOTRAN very well. The comparison between the MIZE results and the experimental results by Kim et al (1999 MEMS '99 pp 296-301) shows that the MIZE results agree with the experimental results much better than the FEM simulation given by Kim et al.