The virtually added mass effect of air on a pre-stressed micro-diaphragm sensor

Abstract

The dynamic response of micro-diaphragms vibrating in contact with the surrounding air is of great interest in numerical applications in transducing, sensing and physical measurements. Therefore, effects of air damping and residual stress on the resonant frequencies of circular micromechanical resonators were theoretically analysed in this paper. Thin circular SiC (100) micro-diaphragms of different dimensions subjected to tensile residual stress were fabricated to validate the theoretical model experimentally. In order to study the added mass effect of air, dynamic properties of the micro-diaphragms vibrating in different air pressure were measured. It was found that the virtually added mass effect played a major role in damping the vibration of a diaphragm in air and the magnitude of air damping accordingly exhibited dependence on the environmental pressure ratio. An increase in this ratio led to a stronger effect of air damping on the diaphragm. Residual stress also had a significant effect on the non-dimensional added virtual mass incremental (NAVMI) factor. The NAVMI factor was found to have a continuous plate-membrane transition behaviour when the residual stress of a diaphragm falls in a certain range.