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

Abstract

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.