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Analysis of Residual Stresses on the Vibration of a Circular Sensor Diaphragm with Surface Effects

  • S.-S. Zhou (a1), S.-J. Zhou (a1), A.-Q. Li (a1) and B.-L. Wang (a2)


Resonant micro-biochemical sensors play important roles in a wide range of emerging applications to detect biochemical molecules. As the resonators of micro-biochemical sensors, the vibration characteristics of circular sensor diaphragms are important for the design of diaphragm-based resonant micro-biochemical sensors. In this paper, the influence of residual stresses on the vibration of a circular sensor diaphragm with surface effects is analyzed. Based on the Kirchhoff's plate theory and surface elasticity theory, the governing equation is presented. The material characteristic lengths for different surface effects are obtained. The influences of residual stresses on the effective flexural rigidity and natural frequency of the diaphragm with surface effects are discussed. Results show that the influence of residual stresses on the effective flexural rigidity becomes obvious with the increasing of residual stresses. The first order natural frequency increases rapidly when the tension parameter is larger than 30 for the stiffened surfaces, while for the softened surfaces the value is 10. Moreover, surface effects can influence the transition range of diaphragm from the plate behavior to membrane behavior in terms of the tension parameter. The transition range can be enlarged by the stiffened surface and be shortened by the softened surface. The analysis and results are helpful for the design of sensor diaphragm-based resonant micro-biochemical sensors and some related researches.


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