Dynamic stability and frequency responses of the tilted curved nanopipes in a supersonic airflow via 2D hybrid nonlocal strain gradient theory

In the presented work, vibrational behavior related to a curved nanopipe which is under supersonic airflow and conveying fluid flow, is examined. To model the size-dependent nanopipe, the Quasi-2D hybrid type of nonlocal strain gradient theory (QHNSGT) is presented. Formulations are obtained by means of Hamilton's principle for bi-directional functionally graded (Bi-FG) nanopipe. Also, formulations are solved by means of the generalized differential quadrature method (GDQM). By taking into account that the fluid flow is infinite, incompressible, uniform flow, Newtonian, laminar, as well, as viscous, and with the help of the Navier-Stokes equation, the fluid structure interaction is obtained. A quasi-2D hybrid type of higher-order shear deformation theory is employed to introduce the displacement fields. The verification section shows that the results of this paper are very near to the results of the published article in the literature. One of the important findings of the current research is critical values of the Mach number could have increased with the aid of increasing the rigidity of edges and decreasing fluid flow velocity. Another marvelous output is that opening angle and airflow stability have an indirect relation, and increasing the opening angle provides an expansion in the unstable area.