Simultaneous determination of position and mass of a particle by the vibration of a diaphragm-based nanomechanical resonator

We present a theoretical analysis of the vibration of a suspended circular diaphragm resonator with a particle at an arbitrary location when considering the effects of plate stiffness and membrane tension in the diaphragm. The analytical expression relating position and mass of a particle attached on a stretched diaphragm with varying residual stress to the resulting shifts in diaphragm resonant frequency is derived. It has been shown that the...