Instability of thermally induced vibrations of carbon nanotubes

The dynamical stability of carbon nanotubes embedded in an elastic matrix under time-dependent axial loading is studied in this paper. The effects of van der Waals interaction forces between the inner and outer walls of nanotubes are taken into account. Using continuum mechanics, we apply an elastic layered shell model to solve the transverse parametric vibrations of a carbon nanotube. Both the Gaussian wide-band axial temperature changes and physically realizable temperature changes with known probability distributions are assumed as the tube axial loading. The energy-like functionals are used in the stability analysis. The emphasis is placed on a qualitative analysis of dynamic stability problem. Stability domains in the space of geometric, material and loading parameters are presented in analytical forms.