Longitudinal vibrations of aluminum nanobeams by applying elastic moduli of bulk and surface: molecular dynamics simulation and continuum model

Abstract

The elastic moduli of the bulk and surface as well as the equivalent mass density are applied to the continuum model of a nanobeam to predict the free longitudinal vibrations of aluminum (Al) nanobeams, especially in cases in which applying the classical theories results in significant errors—i.e. the cross section area of the nanobeams is lower than 4 × 4 nm2. To this end, the bulk elastic modulus and the surface elastic modulus of the Al nanobeam are extracted using surface elasticity theory, a bulk-surface model and molecular dynamics (MD) simulation. These elastic moduli are extracted by several strain values and the results show that the surface elastic modulus is very sensitive to the strain value, so that when the strain value increases from 0.001 to 0.02, the surface elastic modulus decreases significantly while the bulk elastic modulus shows fewer changes. Moreover, the size dependency of the mass density in the continuum nanobeam models is investigated in detail. Also, the natural frequencies of the Al nanobeams are obtained by MD simulation and they are compared with those obtained by the continuum model. Comparisons of the results show that the extracted bulk and surface elastic moduli are acceptable, and that the modified continuum model can predict the dynamic behavior of the Al nanobeam.