  This article is dedicated to the investigation of the stabilization problem
of a flexible beam attached to the center of a rotating disk. We assume that
the feedback law contains a nonlinear torque control applied on the disk and
nonlinear boundary controls exerted on the beam. Thereafter, it is proved that
the proposed controls guarantee the exponential stability of the system under a
realistic smallness condition on the angular velocity of the disk and general
assumptions on the nonlinear functions governing the controls. We used here the
strategy of Lasiecka and Tataru and Alabau-Boussouira. This permits to improve
the stability result shown in \cite{CH:99} in the sense that, on one hand, we
deal with a general form of the nonlinear functions involved in the boundary
controls. On the other hand, we manage to weaken the conditions on those
functions unlike in B. Chentouf and J. F. Couchouron, Nonlinear feedback
stabilization of a rotating body-beam without damping, ESAIM: COCV., 4 (1999),
515-535, where the authors consider a special type of functions that are almost
linear.
