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

• Published in: Physica. E, Low-dimensional systems & nanostructures Vol. 43; no. 8; pp. 1419 - 1426
• Main Authors: Chang, T.-P., Liu, M.-F.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.06.2011; Elsevier
• Subjects: Condensed matter: structure, mechanical and thermal properties; Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Materials science; Mechanical and acoustical properties of condensed matter; Mechanical properties of nanoscale materials; Nanocrystalline materials; Nanoscale materials and structures: fabrication and characterization; Nanotubes; Physics; Numerical computation; Hamiltonians; Fluid flow; Size effect; Van der Waals interaction; Carbon nanotubes; Mechanical properties; Instability; Flow velocity; Elasticity theory; Hopf bifurcation; Nanostructured materials
• ISSN: 1386-9477; 1873-1759
• DOI: 10.1016/j.physe.2011.03.015

Instability occurs in double-walled carbon nanotubes when a fluid flows through them. This is investigated using an elastic shell model based on Donnell's 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. ► The critical flow velocity of the DWCNTs is correlated to the small size effects. ► The nonlocal natural frequencies of DWCNTs decrease as compared to local ones. ► As the flow velocity increases, DWNCTs get through multi-bifurcations in turn.