22. In-Plane Free Vibration and Stability of High Speed Rotating Annular Disks and Rings

Analytical method is presented for the determination of free vibration characteristics of high speed viscoelastic rotating disks. In the development of this analytical solution, two-dimensional elastodynamic theory is employed and the viscoelastic material for the medium is allowed by assuming complex elastic moduli. The general governing equations of motion are derived and a solution for a single rotating disk with different boundary conditions is developed for a wide range of rotating speeds and any radius ratios, such as those for solid disks or thin rings. The proposed solution is used to investigate the influences of hysteretic material damping on dimensionless natural frequencies and modal loss factors for the rotating disks. Furthermore, the solution is expanded to consider the effect of adding disk segment with different material on the inner or outer sides of a disk on the natural frequencies and critical speeds of the equivalent single disk. The dimensionless results for these cases are presented for a wide range of rotational speeds.