On Boundary Damped Inhomogeneous Timoshenko Beams and Related Problems

TL;DR

This paper studies boundary damping in inhomogeneous Timoshenko beams using a first order system approach, including dynamic boundary conditions and various material laws, linking to Sturm-Liouville problems.

Contribution

It introduces a unified first order framework for boundary damping in Timoshenko beams, encompassing diverse material laws and connecting to Sturm-Liouville problems.

Findings

Boundary damping modeled as dynamic boundary conditions.

Inclusion of a wide class of material laws.

Connection to Sturm-Liouville problems with boundary damping.

Abstract

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.