Analytical modeling of squeeze air film damping of biomimetic MEMS directional microphone

• Analytical model of squeeze film damping of directional microphone is derived.
• Modified Reynolds equation and Green׳s function are used in analytical model.
• Analytical model helps us to tune the damping values of the microphone.
• Analytical results are verified with ANSYS results and they are in good agreement.

Squeeze air film damping is introduced in microelectromechanical systems due to the motion of the fluid between two closely spaced oscillating micro-structures. The literature is abundant with different analytical models to address the squeeze air film damping effects, however, there is a lack of work in modeling the practical sensors like directional microphones. Here, we derive an analytical model of squeeze air film damping of first two fundamental vibration modes, namely, rocking and bending modes, of a directional microphone inspired from the fly Ormia ochracea׳s ear anatomy. A modified Reynolds equation that includes compressibility and rarefaction effects is used in the analysis. Pressure distribution under the vibrating diaphragm is derived by using Green׳s function. From mathematical modeling of the fly׳s inspired mechanical model, we infer that bringing the damping ratios of both modes in the critical damping range enhance the directional sensitivity cues. The microphone parameters are varied in derived damping formulas to bring the damping ratios in the vicinity of critical damping, and to show the usefulness of the analytical model in tuning the damping ratios of both modes. The accuracy of analytical damping results are also verified by finite element method (FEM) using ANSYS. The FEM results are in full compliance with the analytical results.

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