Boundary Value Problems
Volume 2006 (2006), Article ID 75107, 14 pages

A transmission problem for beams on nonlinear supports

To Fu Ma1 and Higidio Portillo Oquendo2

1Department of Mathematics, State University of Maringá, Maringá 87020-900, PR, Brazil
2Department of Mathematics, Federal University of Paraná, Curitiba 81531-990, PR, Brazil

Received 20 October 2005; Revised 10 April 2006; Accepted 12 April 2006

Copyright © 2006 To Fu Ma and Higidio Portillo Oquendo. 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.


A transmission problem involving two Euler-Bernoulli equations modeling the vibrations of a composite beam is studied. Assuming that the beam is clamped at one extremity, and resting on an elastic bearing at the other extremity, the existence of a unique global solution and decay rates of the energy are obtained by adding just one damping device at the end containing the bearing mechanism.