Dynamic behavior and stability analysis of fluid-conveying nano-spiral shells: Modeling, simulation, and parametric study

This paper presents a study on a fluid-conveying nano-spiral shell’s free vibration and stability analysis. The nano-spiral shell with Archimedean cross-section shape is modeled according to the first-order shear deformation (FSDT) and modified coupled stress (MCST) theories. Van der Waals force is modeled based on the Leonard Jones potential for atomic interactions. The fluid-structure interaction equation is derived based on the assumption of slip boundary conditions for the fluid. The Rayleigh-Ritz method is used to obtain the natural frequencies of a macro-size spiral shell to be validated with the finite element method (FEM). The parametric vibration analysis is performed for a nano-spiral shell conveying fluid. The results show that the natural frequencies decrease as the distance between the layers of the nano-spiral shell increases. Additionally, an increase in length results in a decrease in natural frequencies. Stability analysis is conducted, and flutter and divergence bifurcations are accurately studied. The results show that the shell with clamped boundary conditions is more stable than the supported boundary condition due to its higher bending stiffness. As the distance between the layers of the fluid-conveying nano-spiral shell increases, instability occurs at a lower fluid velocity. Conversely, as the thickness of the shell increases, the nanostructure becomes unstable at higher fluid velocities.