Size-dependent stability analysis of a functionally graded cylindrical shell subjected to swirling annular flow including the fluid viscosity

Abstract

In this paper, the stability and dynamics of a functionally graded materials (FGMs) cylindrical micro-shell subjected to swirling annular fluid through the annulus between the inner shell and the outer shell are firstly investigated. The fluid perturbation pressure related to the shell vibration is determined by the potential flow theory. The steady viscous forces are derived based on the fully developed turbulent flow. The shell motion equations are established on the basis of the Hamilton's principle along with the Donnell shell theory. To capture the size effect of micro-shell, the zero-level contour method is adopted to obtain the solutions of shell motion equations. First, the system subjected to an ideal annular flow is studied. The results show effects of the fluid rotation, material length-scale parameter, and material properties on the fluid-micro-shell system stability. Furthermore, the coupling effect of the fluid rotation and the material length-scale parameter on the dynamical stability of the system is evaluated. Second, the system subjected to a viscous annular flow is further studied. A more impressive result is observed that the fluid viscosity effect renders the system subjected to an annular flow more unstable, and the physical explanation for the phenomenon is presented.