Spectral properties and stability of a nonselfadjoint Euler-Bernoulli beam

Abstract

In this note we study the spectral properties of an Euler-Bernoulli beam model with damping and elastic forces applying both at the boundaries as well as along the beam. We present results on completeness, minimality, and Riesz basis properties of the system of eigen- and associated vectors arising from the nonselfadjoint spectral problem. Within the semigroup formalism it is shown that the eigenvectors have the property of forming a Riesz basis, which in turn enables us to prove the uniform exponential decay of solutions of the particular system considered.