Stability of a spinning disk under a stationary oscillating unit

The free vibration and elastic stability of a spinning annular plate transversely in contact with a stationary oscillating unit is studied in this paper. The oscillating unit consists of two parallel combinations of springs and dampers attached above and under a mass. Therefore, the displacement of the mass is not the same as that of the disk at the contact point. In this work, the equations of motion of the spinning disk and the oscillating unit in an inertial coordinate system are given first, and the displacement of the disk is expressed in terms of the eigenfunctions of the stationary disk. The Galerkin method is then applied to obtain the discretized system equations for the disk, and these equations are combined with the equation for the oscillating unit. Finally, the stability analysis is conducted by investigating the eigenvalue problem of the combined system. Numerical results show that taking account of the stiffness between the oscillating unit and the disk may bring about extra flutter-type instability between the predominantly oscillating-unit mode and the predominantly reflected disk modes, and these extra unstable regions are much larger than those of the flutter-type instability between different kinds of predominantly disk modes.