Abstract and Applied Analysis
Volume 3 (1998), Issue 3-4, Pages 377-400
Uniform stabilization of a coupled structural acoustic system by
Department of Applied Mathematics, University of Virginia, Thornton Hall, Charlottesville 22903, VA, USA
Received 15 November 1997
Copyright © 1998 Mehmet Camurdan. 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.
We consider a coupled PDE system arising in noise reduction problems. In a two dimensional chamber, the acoustic pressure (unwanted noise) is represented by a hyperbolic wave equation. The floor of the chamber is subject to the action of piezo-ceramic patches (smart materials). The goal is
to reduce the acoustic pressure by means of the vibrations of the floor which
is modelled by a hyperbolic Kirchoff equation. These two hyperbolic equations
are coupled by appropriate trace operators. This overall model differs from those previously studied in the literature in that the elastic chamber floor is here more realistically modeled by a hyperbolic Kirchoff equation, rather than by a parabolic Euler-Bernoulli equation with Kelvin-Voight structural damping, as in past literature. Thus, the hyperbolic/parabolic coupled system of past literature is replaced here by a hyperbolic/hyperbolic coupled model. The main result of this paper is a uniform stabilization of the coupled PDE system by a (physically appealing) boundary dissipation.