Control of Longitudinal Waves in a Rod with Voigt Damping

The control of longitudinal waves in a rod having material damping governed by the Voigt model is considered. Wave-mode coordinate methods are used to derive a relation between the force at a general point in the rod and the force applied to one end of the rod. The force relation includes the effects of a single-input single-output controller which prevents the incoming waves from reaching the other rod end. Two controller design methods - least squares transfer function matching and direct force reduction - are derived. The force relation is used to assess the wave isolating effects of the controller on the structure. Wave isolations greater than 99% are obtained with low order finite dimensional controllers.