Transverse vibration and stability of spinning circular plates of constant thickness and different boundary conditions

The lower approximate natural frequencies of a spinning circular plate are determined for various boundary conditions. The plate is rotating with constant speed of spin about the axis of symmetry perpendicular to its plane. The boundary conditions treated here are: clamped, simply supported, free and guided. It is assumed that the normal displacement of the plate is small and that it does not affect during the oscillation the angular and radial variable stress distribution due to the rotating of the plate. This divides the problem at hand into two parts, of which the first part determines the radial and angular variable planar stresses in the plate, while the second part requires the solution of the partial differential equation with variable coefficients. The approximate lower natural frequencies are determined as functions of the speed of spin and exhibit in the plates with clamped, guided and simply supported boundary conditions instabilities.