PARAMETRIC RESONANCES IN AN ANNULAR DISC, WITH A ROTATING SYSTEM OF DISTRIBUTED MASS AND ELASTICITY - AND THE EFFECTS OF FRICTION AND DAMPING

The parametric resonances that occur in a stationary annular disc unde r the action of a distributed mass-spring-damper system which rotates, with friction, around the disc at subcritical speeds is the main focu s of this paper; The distributed system occupies an annular sector and the stiffness, mass, damping and friction are each expanded in a Four ier series. When the distributed system is rotated then a set of stiff ness, mass, damping and friction terms are obtained that vary both spa tially and temporally. Finite element discretization is applied to the disc and the distributed system and the parametric resonances are det ermined by a multiple time-scales analysis of the finite element equat ions. The equations that define the transition curves are generally co mplex, although they are strictly real when damping and friction are o mitted. Numerical results show that friction has a destabilizing effec t over the entire subcritical speed range. Disc damping and damping in the rotating system both tend to suppress the vibrations of the disc when the speeds are subcritical. The effects of the distributed mass a nd stiffness are found to be almost neutral at subcritical speeds, but active in the supercritical range where the findings of other researc hers are available for comparison and found to be in agreement.