Modeling the longitudinal wave in a nanorod based on a novel theory of elastic waves with surface effects

This paper investigates the impact of surface effects on the propagation behavior of longitudinal waves in a nanorod. A theoretical model has been established on the basis of a newly proposed theory of elastic waves with surface effects. The surface effects comprise two components: the effect of surface energy and the effect of surface inertia. An analytical formula for the longitudinal wave velocity of a nanorod has been derived. Two inherent lengths at nanoscale have been deduced to characterize these two types of surface effects. The results indicate that the longitudinal wave in a nanorod is still nondispersive. However, an attractive phenomenon uncovered is that when the size of a rod reduces to the inherent lengths at nanoscale, the longitudinal wave velocity becomes size-dependent due to the effects of surface energy and surface inertia. The former increases the longitudinal wave velocity, whereas the latter decreases it. This can be understood as the former equivalently increasing the stiffness of the nanorod, whereas the latter enhancing its effective density. On the other hand, when the rod is at the macroscale, the longitudinal wave velocity degenerates to the classical velocity for a macroscopic rod without any surface effects. The current findings not only enhance our understanding of the size-dependent wave velocity of longitudinal waves in nanorods but also facilitate precisely designing the elastic wave nanodevices.