Modeling and experimental characterization of squeeze film effects in nonlinear capacitive circular microplates

In this article, an original approach to model the squeeze film effects in capacitive circular microplates is developed. The nonlinear von Kármán plate theory is used while taking into consideration the electrostatic and geometric nonlinearities of the clamped edge microplate. The fluid underneath the plate is modeled using the nonlinear Reynolds equation with a corrected effective dynamic viscosity due to size effect. The strongly coupled system of equations is solved using the Differential Quadrature Method (DQM) by discretizing the structural and the fluid domains into a set of grid points. The linear effects of the squeeze film on the microplate have been investigated based on the complex eigenfrequencies of the multiphysical problem. It is shown that the air film can alter the resonance frequencies by adding stiffness as well as damping to the system. The model has been validated numerically with respect to a Finite Element Model (FEM) implemented in ANSYS and experimentally on a fabricated circular microplates. The nonlinear effects of the squeeze film have been studied by determining the steady state solution of the system using the finite difference method (FDM) coupled with the arclength continuation technique. It is shown that the decrease of the static pressure shifts the resonance frequency and leads to an increase of the vibration amplitude due to the reduction of the damping coefficient, while the increase in the pressure enlarges the bistability domain. The developed model can be exploited as an effective tool to predict the nonlinear dynamic behavior of microplates under the effect of air film for the design of Capacitive Micromachined Ultrasonic Transducers (CMUTs).