K. T. Andrews, J.R. Fern\'andez and M. Shillor,

We present and investigate a model for the thermomechanical behaviour
of a viscoelastic beam with an attached tip body. The model consists of a
coupled energy-elastic system of equations for the beam together with an
equation for the temperature of the tip body. We establish existence and
uniqueness of a weak solution to the system. We also propose a finite element
algorithm for solutions to the system and present numerical simulations based
on the algorithm.