Modeling of nanofabricated paddle bridges for resonant mass sensing

The modeling of nanopaddle bridges is studied in this article by proposing a lumped-parameter mathematical model which enables structural characterization in the resonant domain. The distributed compliance and inertia of all three segments composing a paddle bridge are taken into consideration in order to determine the equivalent lumped-parameter stiffness and inertia fractions, and further on the bending and torsion resonant frequencies. The approximate model produces results which are confirmed by finite element analysis and experimental measurements. The model is subsequently utilized to quantify the amount of mass which attaches to the bridge by predicting the modified resonant frequencies in either bending or torsion