The radial dynamics of a single-walled zigzag carbon nanotube under pulsed pressure is studied. Uniform external pressure is applied instantly, then remains constant for a certain time, and then is instantly released. This loading scheme allows one to consider a carbon nanotube under plane strain conditions and replace it with a circular ring formed by one zigzag row of carbon atoms. The bending deformation of the ring in its plane is described by an equation based on the Kirchhoffs hypothesis. An effective parameter is used, including the bending stiffness of the ring and areal density. The regimes of oscillatory motion and exponential growth of radial displacements are investigated depending on the magnitude and duration of the applied pressure. Alternatively, the ring is analyzed in terms of a molecular dynamics model with a reduced number of degrees of freedom, taking into account the plane strain conditions. With the help of molecular dynamics, the limits of the thin shell theory are established. For (n, 0) CNTs with n > 15, in the regime of small-amplitude vibrations, the discrepancy between the continuum model and molecular dynamics calculations does not exceed 5% and decreases with increasing n.

The problem of parametric identification of a two-dimensional nanocrystalline medium consisting of circular particles arranged in a hexagonal lattice is considered. Differential equations are derived that describe propagation of acoustic and rotational waves in this medium. It is shown that, due to dispersion dependencies, microstructure parameters and moduli of elasticity of the nanocrystalline medium can be estimated from measured wave propagation velocities.