dc dynamic and static pull-in predictions and analysis for electrostatically actuated clamped circular micro-plates based on a continuous model

This study develops a continuous model to analyze the ‘pull-in’ effect in the circular micro-plates used in capacitive-type micro-electro-mechanical systems (MEMS) sensors, actuators and microphones. In developing the model, the governing equation of motion of the deformed plate is established in the form of a partial different equation (PDE) which is then decomposed using the Galerkin method to create a coupled set of modal ordinary differential equations. By considering the first-order deflection mode only and using a fifth-order Taylor series expansion of the electrostatic force, closed-form solutions are obtained for both the position and the voltage of the static pull-in event. Applying an energy balance method and a finite-order approximation method, the solutions are then obtained for the position and voltage of the dynamic pull-in event. The theoretical results obtained for the pull-in phenomena are verified based on the comparison to available experimental data, and also numerically using a finite element analysis (FEA) approach. In general, the results indicate that the ratio of the dynamic to static pull-in voltages is approximately 92%. However, when the squeezed-film effect induced by the air gap between the two plates is taken into account, the value of this ratio increases slightly as a result of considering a higher dynamic pull-in voltage. (Some figures in this article are in colour only in the electronic version)