Analyzing thin film damping in a rotary comb-drive resonator considering slip boundary conditions

In this paper, thin film damping in a rotary comb-drive resonator has been investigated. The proposed model for this study is made up of a rigid oscillating finger in a plate form suspended between two fixed fingers. The micro-gap between the vibrating finger and the fixed fingers is filled with air. Equations of motion governing the longitudinal vibration of the micro finger and the fluid field have been extracted considering reasonable assumptions. The coupled partial differential equations have been non-dimensionalized, discretized and solved simultaneously utilizing Galerkin-based Reduce order model. As the gap between the fingers is so small and comparable to the dimensions of the air molecules, the slip boundary condition is considered at the solid-fluid interface. Complex frequency approach is applied to predict the equivalent quality factor of the resonator. The effect of geometrical parameters of the resonator as the length, thickness and the fluid gap on the equivalent damping ratio of the resonator has been investigated. It has been shown that slip boundary conditions causes the freedom of the fluid motion at the boundaries to increase which results in increment of the quality factor of the resonator