  This paper presents the stability analysis of a system composed of rotating
beams on a flexible, circular fixed ring, using the Routh-Hurwitz criterion.
The model displayed has been fully developed within the rotating frame by use
of an energy approach. The beams considered possess two degrees of freedom
(dofs), a flexural motion as well as a traction/compression motion. In-plane
deformations of the ring will be considered. Divergences and mode couplings
have thus been underscored within the rotating frame and in order to simplify
understanding of all these phenomena, the dofs of the beams will first be
treated separately and then together. The dynamics of radial rotating loads on
an elastic ring can create divergence instabilities as well as post-critical
mode couplings. Moreover, the flexural motion of beam rubbing on the ring can
also lead to mode couplings and to the locus-veering phenomenon. The presence
of rubbing seems to make the system unstable as soon as the rotational speed of
the beams is greater than zero. Lastly, the influence of an angle between the
beams and the normal to the ring's inner surface will be studied with respect
to system stability, thus highlighting a shift frequency phenomenon.
