Riesz Basis Generation of a Beam Equation with Generalized Viscous Damping

In this paper, the Riesz basis analysis for a Euler-Bernoulli beam equation with generalized viscous damping is conducted. By using Guo's conclusion that the Riesz basis property holds for the general system if its associated characteristic equation is strongly regular, it is shown that the Riesz basis property can be established for a beam equation with generalized viscous damping. Furthermore, we get the conclusions that the system operator A generates a C-0-semigroup e(At) on state space and the spectrum-determined growth condition holds : s(A) = omega(A).