A differential equation that is generally effective for squeeze film air damping of perforated plate and non perforated plate as well as in MEMS devices is developed.For perforated plate,the thickness and the dimensions of the plate are not limited.With boundary conditions,pressure distribution and the damping force on the plate can be found by solving the differential equation.Analytical expressions for damping pressure and damping force of a long strip holeplate are presented with a finite thickness and a finite width.To the extreme conditions of very thin plate and very thin hole,the results are reduced to the corresponding results of the conventional Reynolds' equation.Thus, the effectiveness of the generalized differential equation is justified.Therefore,the generalized Reynolds' equation will be a useful tool of design for damping structures in MEMS.
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.
