Mode dependent fluid damping in pre-stressed micro-diaphragm resonators

Abstract

This paper presents a theoretical model, based on the Rayleigh-Ritz method, to analyze the dynamic response of circular micro-diaphragms in contact with a fluid. The fluid is assumed to be incompressible, inviscid, and irrotational. In the model, a linear combination of polynomials is utilized to construct the mode shapes, and the Rayleigh quotient for fluid-structure coupling system is implemented to obtain the dynamic characteristics of pre-stressed diaphragms. Theoretical calculations are well validated by a finite element model. The relationships of the natural frequencies and quality factors to the mode shape are systematically investigated. The investigation proves that it is necessary to adopt exact mode shapes, instead of approximate mode shapes, to ensure the accuracy in the theoretical evaluation of the vibration of the diaphragm in the fluid. Furthermore, the quality factor associated with acoustic radiation losses is mode dependent, and its dependency on the mode number shows plate, membrane, and plate-membrane transition behaviors as pre-stress varies. These findings can be useful in the applications of diaphragm-based resonators