具有扭转耦合效应的复合薄壁梁黎斯基的性质和指数稳定性(英文)

研究了具有扭转耦合效应的复合薄壁梁黎斯基的性质以及指数稳定性.首先证明该系统决定算子的预解式是紧的,且可生成群.其次,通过对该系统算子谱的渐近分析,证明了除至多有限个本征值外,其算子的谱是单重可分离的.特殊地,我们获得了自由系统的频率渐近表达式,因而利用克尔德什定理,证明了在希尔伯特状态空间中算子广义本征函数列的完备性.最后,结合黎斯基的性质及算子谱的分布证明了该系统的指数稳定性.

Riesz Basis Property and Exponential Stability of Composite Thin-walled Beams with Torsion Coupled Effect

In this paper we study Riesz basis property and exponential stability of a composite thin wall beam with torsion coupled effect.Firstly we show that the operator determined by the system is of compact reeolvent and generates a Co group.Second,by the asymptotic analysis of spectrum of the system operator,we shown that the spectrum of the operator are separated and simple except at most finite number of eigenvalues.As a special case,we obtain the asymptotic expression of frequencies of the free system,and hence applying Keldysh theorem,we prove that the generalized eigenfunctions of the operator is complete in the state Hilbert space.In addition,applying an obtained result,we get that there is a sequence of generalized eigenfunetions of the operator that forms a Riesz basis for state Hilbert space.Finally,from the Riesz basis property and the distribution of spectrum of the operator we assert the exponential stability of the system.