Mass detection in nanobeams from bending resonant frequency shifts

Nanobeams are frequently used as vibration based-sensors to detect mass changes caused, for instance, by attachment of foreign atoms/molecules or chemical/molecular absorption. This paper deals with the bending vibration of a uniform nanobeam carrying a single point mass (direct problem) as well as the identification of the attached mass (inverse problem). The nanobeam is described using the modified strain energy theory adapted to the Euler-Bernoulli beam model, and the natural vibration frequencies have been obtained. Under the assumption of small intensity of the concentrated mass, a solution of the inverse problem based on the measurement of the mass-induced shifts in the first two eigenfrequencies is proposed. Both the cases of simply supported and cantilever end conditions are discussed in detail. The theoretical method is verified by numerical simulation and numerical tests agree well with analytical results.