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Journal of Applied Mathematics
Volume 2014, Article ID 298092, 7 pages
http://dx.doi.org/10.1155/2014/298092
Research Article

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

Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

Received 22 January 2014; Revised 11 April 2014; Accepted 11 April 2014; Published 15 May 2014

Academic Editor: Francisco J. Marcellán

Copyright © 2014 M. Basson et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a model for the vibration of a beam with 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.