Analyticity and Riesz basis property of semigroups associated to damped vibrations

By Birgit Jacob, C. Trunk, M. Winklmeier. 2007

48 citations recorded by the source corpus.

Abstract.Second order equations of the form $$\ddot{z}(t) + A_0z(t) + D\dot{z}(t) = 0$$ 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 $$\mathcal{A} = \left[ {\begin{array}{*{20}c} 0 & I\\ { -A_0 } & { -D}\\ \end{array}} \right]$$ 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 $${\mathcal{A}}$$ in the phase space.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/95ed1698c8773ec8cea7604fde44ffc35f27c995

Citations in the corpus

• A structurally damped plate equation with Dirichlet-Neumann boundary conditions (2015, unknown): “[5], [20], [23], [29] and the references therein.”