Abstract: A differential equation for calculating squeeze-film air damping in slotted plates is developed by modifying the Reynolds equation.A term is added to account for the effect of airflow through the slots on the air damping of the plate.The end effect of the airflow in the slots is also treated by substituting an effective channel length for the geometric channel length (i.e.the thickness of the plate).The damping pressure distribution,damping force,and damping force coefficient of the slotted plates can be found by solving the equation under appropriate boundary conditions.With restrictions on the thickness and the lateral dimensions of the slotted plate removed,the equation provides a useful tool for analysing the squeeze-film air damping effect of slotted plates with finite thickness and finite lateral dimensions.For a typical slotted plate structure,the damping force coefficient obtained by this equation agrees well with that generated by ANSYS.

Key words: squeeze-film air damping, MEMS, slotted plate, Reynolds equation