Analysis of Stability for n-Connected Timoshenko Beams with Both Ends Fixed and Feedback Controller at Intermediate Nodes
两端固定n根系列连接的Timoshenko梁在连接点加控制的镇定问题

The stabilization problem of $n$-connected Timoshenko beams is studied. Suppose that both ends of the beams are claped, and at intermediate nodes, theshearing force and bending moment are continuous, but the displacement and rotational angle of beams are discontinuous. Shearing force and bending moment at intermediate nodes can be observed. The compensators are designed to obtain the displacements and rotational angles, and the feedback controllers at intermediate nodes are designed to stabilize the system. It is shown that the closed loop system is asymptotically stable. By a lengthy spectral analysis of the system, it is proven that the closed loop system is of Riesz basis property under some conditions. Hence, the spectrum determined growth condition holds.