Dynamics and Stability Analysis of Rotating Cylindrical Shells in Annular Fluid Medium

Stability and dynamics of rotating coaxial cylindrical shells conveying incompressible and inviscid fluid are investigated. The interior shell is assumed to be flexible while the exterior cylinder is rigid. Using Sander's-Koiter theory assumptions and following Hamilton's principle, governing equations of motion are determined in their integral form. Employing the extended Galerkin method of solution, the integral equations of motion are projected to their equivalent system of algebraic equations. Fluid equations are fundamentally based on the linearized inviscid Navier-Stokes equations. Impermeability condition on the fluid and structure interface as well as the zero radial velocity component on the exterior shell give the coupled equations of motion governing the dynamics of fluid-loaded coaxial cylindrical shells. Using the coupled fluid-structural model, stability boundaries are determined for the rotating interior shell. Various parameter studies are conducted and effects of mass ratio, gap distance between the interior and exterior shells, boundary conditions of the interior shell, length to radius ratio on the stability margins are thoroughly investigated and reported.