Boundary Value Problems 
Volume 2006 (2006), Article ID 75107, 14 pages
doi:10.1155/BVP/2006/75107

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

Abstract

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.