On Boundary Damped Inhomogeneous Timoshenko Beams and Related Problems
  We consider the model equations for the Timoshenko beam as a first order system in the framework of evolutionary equations. The focus is on boundary damping, which is implemented as a dynamic boundary condition. A change of material laws allows to include a large class of cases of boundary damping. By choosing a particular material law, it is shown that the first order approach to Sturm-Liouville problems with boundary damping is also covered. 
Rainer Picard, Bruce A. Watson
math.AP