Scale effects on the longitudinal wave propagation in nanoplates

In this paper, the propagation characteristics of the longitudinal wave in nanoplates with small scale effects are studied. The equation of the longitudinal wave is obtained using the nonlocal elastic theory. The phase velocity and the group velocity are derived, respectively. The dispersion relation is analyzed with different wave numbers and scale coefficients. It can be observed from the results that the dispersion properties of the longitudinal wave are induced by the small scale effects, which will disappear in local continuous models. The dispersion degree can be strengthened by increasing the scale coefficient and the wave number. Furthermore, the characteristics for the group velocity of the longitudinal wave in nanoplates can also be tuned by these factors.