Flow-induced instability of double-walled carbon nanotubes based on nonlocal elasticity theory

Instability occurs in double-walled carbon nanotubes when a fluid flows through them. This is investigated using an elastic shell model based on Donnellʹs shell theory. The dynamic governing equations of double-walled carbon nanotubes are derived on the basis of nonlocal elasticity theory, and the van der Waals interaction between the inner and outer walls is considered. Instability induced by a pressure-driven steady flow is studied. The numerical computations reveal that as the flow velocity increases, double-walled carbon nanotubes have a destabilizing style to get through multi-bifurcations of the first (pitchfork) and second (Hamiltonian Hopf) bifurcations in turn. It can be concluded that the critical flow velocity of the flow-induced instability is closely correlated to the ratio of the length to the radius of double-walled carbon nanotubes, the pressure of the fluid and the small size effects.