Dynamic stability of carbon nanotubes

The dynamical stability of carbon nanotubes embedded in an elastic matrix under time-dependent axial loading is studied in this paper. Effects of van der Waals interaction forces between the inner and outer walls of nanotubes are taken into account. Using continuum mechanics an elastic beam model is applied to solve the transverse parametric vibrations of two co-axial carbon nanotubes. The physically realizable forces with known probability distributions and uniformly distributed on the both beam edges are assumed as the tube axial loadings. The energy-like functionals are used in the stability analysis. The emphasis is placed on a qualitative analysis of dynamic stability problem. Influence of constant component of axial forces on stability regions is shown. Boundaries of dynamic stability regions are determined using the three models and techniques with different degree of accuracy.