The Free Vibrations of a Spinning Centrally Clamped Shallow Spherical Shell

Abstract

The results of a numerical analysis of the free-vibration characteristics of a thin shallow spherical shell spinning about its polar axis are presented. The shell is fully clamped by a central hub. The static equilibrium equations are formulated allowing for finite rotations. The free-vibration equations are derived by considering small perturbations about the spinning equilibrium configuration. Both flexural rigidity and membrane restoring forces due to spin are considered. Known techniques for the solution of stationary shell problems are extended to the more difficult case of the spinning shell. Plots of transverse frequency as a function of shell geometry are presented for the first two modes for shells with one and two nodal diameters for various values of inertia loading. Continuous transition from shell to flat disk results with increasing shell radius of curvature is shown.