Effects of residual stress and fluid loading on vibrations of a micro-diaphragm on a free fluid surface

In this paper, we propose a straightforward theoretical model to examine free vibrations of circular diaphragms subjected to residual stress vibrating on a free fluid surface, which is infinite in the radial direction. An incompressible and inviscid fluid is assumed, and its movement is considered to be insignificant. The mode shapes and resonant frequencies of the diaphragm are determined by the Rayleigh–Ritz approach, taking fluid–diaphragm coupling and residual stress into consideration. We also establish a finite element model to demonstrate the accuracy of the numerical calculation. The analysis shows the residual stress and fluid loading influences on the mode shapes, the natural frequencies, the non-dimensional added virtual mass incremental factors, and the mass sensitivities of the diaphragms. The proposed framework will shed new light on the fundamental understanding of numerous applications involving resonating sensors in contact with the surrounding fluid in a broad sense.