Free vibrations of sensor diaphragm with residual stress coupled with liquids

The free vibrations of a micro-biochemical sensor diaphragm with residual stress in contact with a liquid are analyzed using the Rayleigh-Ritz method in the paper. A mechanics model based on a plate with residual stress is presented and analyzed when the plate vibrates in contact on one side with a liquid. The liquid is assumed to be incompressible and inviscid and the velocity potential is used to describe its irrotational motion. The Ritz solution is performed to find out the dependency of the natural frequency and the mode shape on the residual stress when the diaphragm vibrating in contact with a liquid. The results show that the residual stress significantly affects the natural frequency and the mode shape, and this is important to consider in the research and development of circular biochemical sensor diaphragms.