Stability of a tree-shaped network of strings and beams

In this paper we study the stability of a tree-shaped network of elastic strings and beams with some feedbacks at the ends. The whole system is asymptotically stable. Moreover, the energy of the solution decay exponentially to zero if there is no beam following a string ( from the root to the leaves) and decay polynomially if not. We use a frequency domain method from the semigroups theory.