A nonlocal strain gradient theory for vibration and flutter instability analysis in rotary SWCNT with conveying viscous fluid

In this article, the influence of flow velocity and rotational speed on instability and free vibration analysis of a rotating viscoelastic single wall carbon nanotube (SWCNT) conveying viscous fluid flow is studied. These effects are investigated using a first-order shear deformation cylindrical shell model in the framework of the nonlocal strain gradient theory (NSGT). Due to the rotation, Coriolis Effect, centrifugal and initial hoop tensions are taken into account. The viscous fluid flow relations are inserted into equations of motion via the modified Navier-Stokes relation and slip boundary condition. Finally, governing equations are solved by the generalized differential quadrature method for simply supported and clamped-clamped boundary conditions. The novelty of this study is using the NSGT for such a model which considers both material length scale parameter and nonlocal parameter in the formulation. Furthermore, the effects of the material length scale, nonlocal parameter, viscoelastic constant and boundary conditions on critical flow velocity and critical rotational speed are investigated.