Boundary feedback stabilization of nonlinear beam models

In this paper we consider the large amplitude planar motion of a cantilevered beam with a feedback force and/or torque (proportional and acting opposite to the velocity/angular velocity respectively) applied at the free end. We derive nonlinear equations of motion for such a beam based upon certain natural geometric assumptions. We then prove the existence of weak solutions for these equations, and that a particular class of weak solution is uniformly exponentially stable.