Free vibration and stability of a spinning disk-spindle system

This work examines the free vibration and stability of a spinning, elastic disk-spindle system. The extended operator formulation is exploited to disc retize the system using Galerkin's method (Parker, 1999). The coupled vibra tion modes of the system consist of disk modes, in which the disk dominates the system deformation, and spindle modes, in which the spindle dominates the system deformation. Both the natural frequencies and vibration modes ar e strongly affected by disk flexibility. If the membrane stresses associate d with disk rotation are neglected then the system exhibits flutter instabi lities, but these instabilities are not present when membrane stresses are modeled. Natural frequency veering between disk and spindle frequencies is prominent at low speeds and substantially affects the spectrum and stabilit y. No veering is observed at high speeds where rotational stress stiffening diminishes disk-spindle coupling and causes the natural frequencies to con verge to those of a rotating spindle carrying a rigid disk. Changes to the vibration modes are examined in terms of a strain energy ratio measuring th e contribution of the disk strain energy to the total modal strain energy.