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

Abstract

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 resolvent and generates a C_0 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 eigenfunctions 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.