Guo-Jin Tang

Resonance frequency and mass identification of zeptogram-scale nanosensor based on the nonlocal beam theory

Free vibration and mass detection of carbon nanotube-based sensors are studied in this paper. Since the mechanical properties of carbon nanotubes possess a size effect, the nonlocal beam model is used to characterize flexural vibration of nanosensors carrying a concentrated nanoparticle, where the size effect is reflected by a nonlocal parameter. For nanocantilever or bridged sensor, frequency equations are derived when a nanoparticle is carried at the free end or the middle, respectively. Exact resonance frequencies are numerically determined for clamped-free, simply-supported, and clamped-clamped resonators. Alternative approximations of fundamental frequency are given in closed form within the relative error less than 0.4%, 0.6%, and 1.4% for cantilever, simply-supported, and bridged sensors, respectively. Mass identification formulae are derived in terms of the frequency shift. Identified masses via the present approach coincide with those using the molecular mechanics approach and reach as low as 10(-24)kg. The obtained results indicate that the nonlocal effect decreases the resonance frequency except for the fundamental frequency of nanocantilever sensor. These results are helpful to the design of micro/nanomechanical zeptogram-scale biosensor.

Size-dependent resonance frequencies of longitudinal vibration of a nonlocal Love nanobar with a tip nanoparticle

Axial free vibration of a nanobar carrying a nanoparticle is studied based on the nonlocal elasticity theory and Love’s assumption. By considering inertia of radial motion during longitudinal vibration, a governing equation for a nanobar–mass oscillation system is derived via Hamilton’s principle. An exact frequency equation is obtained and an approximate simple expression for the fundamental-mode resonance frequency is given. The size effect of the resonance frequencies is elucidated. The classical Love bar theory and the nonlocal bar theory can be recovered from two special cases by setting the nonlocal parameter and Poisson’s ratio to zero, respectively. Numerical examples are given to show the influence of the nonlocal scaling parameter and attached mass on the resonance frequencies and frequency shifts. Identification formulas for estimating the mass of an attached nanoparticle and predicting the nonlocal parameter are established through the frequency change.