Stabilization and Riesz basis property of two serially connected Timoshenko beams system.

In this paper we study the stabilization problem and Riesz basis property of two serially connected Timoshenko beams whose left end is simply supported and the right end is free. Suppose that the displacement and bending moments of the beams at the interior node are continuous, but the shearing force and rotational angle are discontinuous. We design the compensator and feedback controllers at the left end and the interior node of the beams so as to derive the beams back to their equilibrium position. We prove that this closed loop system is well-posed and asymptotically stable. By the spectral analysis, we also show that its root vectors form a Riesz basis with parentheses for the state space. Hence the spectrum determined growth condition holds. Further, we show that this system is not exponentially stable. Finally, we give a numerical simulation of this kind of closed loop system to support our results. [ABSTRACT FROM AUTHOR]