Monitoring mass changes using nanoresonator sensors

Abstract

Nanoresonators consisting in a one-dimensional vibrating structure have remarkable performance in detecting small adherent masses. The mass sensing principle is based on monitoring the resonant frequency shifts caused by unknown attached masses. In spite of its important application, few studies are available on this inverse problem. In this work, we have developed a distributed mass reconstruction method in an initially uniform nanobeam under bending vibration, by using finite eigenfrequency data belonging to one spectrum corresponding to supported end conditions. To avoid trivial non-uniqueness due to the symmetry of the initial configuration of the nanobeam, it is assumed that the mass variation has support contained in half of the axis interval. The nanobeam is modelled using the modified strain gradient elasticity accounting for size effects. The reconstruction is based on an iterative procedure, which takes advantage of a closed-form solution when the mass change is small, and shows to be convergent under this assumption. The identification method performs well even for not necessarily small mass changes, and in presence of errors on the data.