Air damping in micro-beam resonators

To research the effect of air damping on resonators, based on the Euler-Bernoulli assumption, beam vibration mechanism and air damping theory, a vibration equation was established and its solution was obtained according to corresponding boundary conditions. The air damping influences on the resonant frequency and quality factor of a micro-beam resonator were obtained under two different conditions. By analyzing air damping in two different ways, it is found that a critical squeeze-film thickness exists under the condition that the aspect ratio of the beam is constant, and the obtained expression of critical thickness can give some suggestions to devices designing.