Solvability of a Model for the Vibration of a Beam with a Damping Tip Body

We consider a model for the vibration of a beamwith a damping tip body that appeared in a previous article. In this paper we derive a variational form for the motion of the beam and use it to prove that the model problem has a unique solution. The proofs are based on existence results for a general linear vibration model problem, in variational form. Finite element approximation of the solution is discussed briefly.