Precise measurement of a concentrated mass and its position by the vibration of a rectangular micro-diaphragm

Abstract

Free vibration of a micro-diaphragm was firstly solved using the Rayleigh–Ritz method by constructing the mode shape as combinations of the clamped-clamped beam functions in width and length directions. An asymptotic solution to the inverse problem of the dynamic system of the diaphragm with a concentrated mass was then derived. It was found that the rectangular micro-diaphragm delivers a unique capability to simultaneously measure the concentrated mass and its position from the observed frequency changes. The proposed strategy in mass sensing was validated by extracting the concentrated mass and its position using simulated and experimental results on a micro-diaphragm resonator.