  In this article, a semianalytical approach for demonstrating elastic waves
propagation in nanostructures has been presented based on the modified
couple-stress theory including acceleration gradients. Using the experimental
results and atomic simulations, the static and dynamic length scales were
calculated for several materials, zinc oxide (ZnO), silicon (Si), silicon
carbide (SiC), indium antimonide (InSb), and diamond. To evaluate the predicted
static and dynamic length scales as well as the presented model, the natural
frequencies of a beam in addition to the phase velocity and group velocity of
Si were studied and compared with the available static length scales, estimated
using strain-gradient theory without considering acceleration gradients. These
three criteria, natural frequency, phase velocity, and group velocity, show
that the presented model is dynamically stable even for larger wavevector
values. Furthermore, it is explained why the previous works, which all are
based on the strain-gradient theory without acceleration gradients, predicted
very small values for the static length scale in the longitudinal direction
rather than the static length scale in the transverse directions.
