Open Access
1998 Uniform stabilization of a coupled structural acoustic system by boundary dissipation
Mehmet Camurdan
Abstr. Appl. Anal. 3(3-4): 377-400 (1998). DOI: 10.1155/S108533759800061X


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.


Download Citation

Mehmet Camurdan. "Uniform stabilization of a coupled structural acoustic system by boundary dissipation." Abstr. Appl. Anal. 3 (3-4) 377 - 400, 1998.


Published: 1998
First available in Project Euclid: 8 April 2003

zbMATH: 0966.93056
MathSciNet: MR1749417
Digital Object Identifier: 10.1155/S108533759800061X

Primary: 35L05 , 93C20

Keywords: boundary dissipation , Coupled structural acoustic system , uniform stabilization

Rights: Copyright © 1998 Hindawi

Vol.3 • No. 3-4 • 1998
Back to Top