Stabilization of Euler-Bernoulli beam by nonlinear boundary feedback

We study the damping of transversal vibrations of a system of non-homogeneous connected Euler-Bernoulli beams. Controls are forces or torques applied at one end of the system. These controls are assumed to be nonlinear functions of the observed velocities of deflection. We show that the problem is well-posed and that asymptotic stability is achieved when the nonlinear feedback is monotone dissipative. No assumption involving monotonicity in the bending moment or linear mass distributions is necessary.