Critical speeds and the response of a spinning disk to a stationary load using Mindlin plate theory

The critical speeds of a moderately thick circular spinning disk are determined using the Mindlin plate theory, which includes shear deformation and rotational inertia. A combination of analytical and numerical methods is used to calculate the four lowest critical speeds for a centrally clamped uniform circular disk and for different thicknesses and clamping ratios. Comparisons between the critical speeds and the corresponding critical speeds for the classical theory, which neglects shear deformation and rotational inertia, are made. The displacement response at the position of the applied force is also determined for different thickness and clamping ratios and compared with the corresponding results from the classical case.