A hinged network of Euler-Bernoulli beams under feedback controls

In this paper, we design boundary feedback controllers at the interior node to stabilize a star-shaped network of Euler-Bernoulli beams. The beams are hinged each other, that is, the displacements of the structure are continuous but the rotations of the beams are not continuous. The well-posed-ness of the closed loop system is proved by the semigroup theory. We show that the system is asymptotically stable if we impose a shear control on the common vertex. Finally, we derive the exponential stability of the system.