Analysis of stability for n-connected Timoshenko beams with both ends fixed and feedback controller at intermediate nodes

In this paper we study stabilization problem of n-connected Timoshenko beams. Suppose that both ends of the beams are clamped, at intermediate nodes, the shearing force and bending moment are continuous, but the displacement and rotational angle of beams are discontinuous. Shearing force and bending moment at intermediate nodes are observed. The compensators are signed to use to obtain the displacements and rotational angles, the feedback controllers at intermediate nodes are used to stabilize the system. We prove that the closed loop system is usually asymptotically stable. By a detail spectral analysis of the system, we show that the closed loop system is of Riesz basis property under some conditions.