Vibrations and stability of a flexible disk rotating in a gas-filled enclosure—Part 1: Theoretical study

The vibrations and linear stability of a flexible disk rotating at sub- and supercritical speeds, and coupled to the acoustic oscillations of the surrounding fluid are investigated theoretically. The surrounding fluid is contained in a cylindrical enclosure. The coupled gyroscopic system equations are formulated using a Kirchhoff plate model for the disk, and the wave equation for the compressible fluid. The formulation includes systematically the effects of geometric perturbations such as radial clearances and asymmetric disk positioning, as well as bulk rotating fluid flows driven by fluid viscosity and disk rotation. A rigorous spatial discretization of this coupled gyroscopic system leads to a singular generalized non-Hermitian eigenvalue problem for which a special computational treatment is presented. The underlying physics of acoustic–structure coupling in the presence of these effects is complex—acoustic oscillations of the fluid above and below the disk couple through disk vibrations and through the radial clearance, while the bulk fluid rotation splits the acoustic modes into forward and backward traveling waves. Flutter instabilities arising from acoustic–structure mode coalescence and various damping mechanisms are discussed. The predictions reveal significant influences of radial clearance, asymmetric disk positioning, and bulk fluid rotation on the vibration and acoustic characteristics of the system that are likely to be observed in experiments, and in practical applications such as in CD/DVD drives and hard disk drives.