Analytical modeling of squeeze-film damping for perforated circular microplates

Predicting squeeze-film damping due to the air gap between the vibrating microstructure and a fixed substrate is crucial in the design of microelectromechanical system (MEMS). The amount of squeeze-film damping can be controlled by providing perforations in microstructures. In the past, to include perforation effects in squeeze-film damping calculations, many analytical models have been proposed. However, only the rectangular perforated microplates are considered in the previous works. There is lack of works that model the squeeze-film damping of circular perforated microplates. In fact, the circular perforated microplates are also common elements in MEMS devices.In this paper, the squeeze-film damping in a perforated circular rigid microplate is modeled using a modified Reynolds equation that includes compressibility and rarefaction effect. The pressure distribution under the vibrating plate is obtained using the Bessel series. Analytical expressions for the squeeze-film damping and spring constants have been found. For a flexible perforated circular microplate, based on Reyleigh’s method, this paper presents an approximate model to estimate the squeeze-film damping in the flexible plate vibrating in the fundamental mode. The accuracy of the present models is verified by comparing its results with the finite element method (FEM) results.