Riesz basis property of the generalized eigenvector system of a Timoshenko beam

The Riesz basis property of the generalized eigenvector system of a Timoshenko beam with boundary feedback controls applied to two ends is studied in the present paper. The spectral property of the operator A determined by the closed loop system is investigated. It is shown that operator A has compact resolvent and generates a C0 semigroup, and its spectrum consists of two branches and has two asymptotes under some conditions. Furthermore it is proved that the sequence of all generalized eigenvectors of the system principal operator forms a Riesz basis for the state Hilbert space.