Flow-induced vibration and instability of embedded double-walled carbon nanotubes based on a modified couple stress theory

Vibration and instability of fluid-conveying double-walled carbon nanotubes (DWNTs) are investigated in this paper based on the modified couple stress theory and the Timoshenko beam theory. The microstructure-dependent Timoshenko beam model, which contains a material length scale parameter and can take the size effect into account, is employed. The Poisson's ratio effect is also included in this model. The surrounding elastic medium is described as the Winkler model characterized by the spring. The higher-order governing equations and boundary conditions are derived by using Hamilton's principle. The differential quadrature (DQ) method is employed to discretize the governing equations, which are then solved to obtain the resonant frequencies of fluid-conveying DWNTs with different boundary conditions. A detailed parametric study is conducted to study the influences of length scale parameter, Poisson's ratio, spring constant, aspect ratio of the DWNTs, velocity of the fluid and end supports on the vibration and flow-induced instability of DWNTs. Results show that the imaginary component of the frequency and the critical flow velocity of the fluid-conveying DWNTs increase with increase in the length scale parameter.

Research highlights
► The imaginary components of the frequencies increase with increase in the length scale parameter.
► The critical flow velocity of the DWNTs increases as the length scale parameter increases.
► DWNTs with large aspect ratio are more likely to cause the divergence instability.