Analyticity and Riesz basis property of semigroups associated to damped vibrations

Second order equations of the form z(t)+A0z(t)+D z(t)=0 are considered. Such equations are often used as a model for transverse motions of thin beams in the presence of damping. We derive various properties of the operator matrix A = 0 I −A0 −D associated with the second order problem above. We develop sufficient conditions for analyticity of the associated semigroup and for the existence of a Riesz basis consisting of eigenvectors and associated vectors of A in the phase space.