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文章研究两端固定n根系列连接的Timoshenko梁系统的镇定问题,假设该系统在连接点处剪切力和弯曲力矩是连续的,而横向位移和旋转角度是不连续的.在连接点处设置控制器,观测节点处的力,通过补偿器补偿后反馈回系统,构成闭环系统.通过对系统的矩阵化处理,对算子谱采用渐近分析的技巧,证明得到该闭环系统是渐近稳定的.并利用算子谱的分布等性质,在一定条件下得到了闭环系统的Riesz基性质,从而系统满足谱确定增长条件.
In this paper, we study the stabilization problem of Timoshenko beam system with n series connections fixed at both ends. Suppose that the shear force and bending moment of the system are continuous at the connection point, while the lateral displacement and rotation angle are discontinuous. Controller and observing node, compensated by the compensator and fed back to the system to form a closed-loop system.Asymptotic analysis of the operator spectrum is made by matrixizing the system, and the closed-loop system is proved to be asymptotically stable The Riesz basis property of the closed-loop system is obtained under certain conditions by utilizing the properties of the operator spectral distribution, and the system satisfies the spectrum to determine the growth conditions.