Abstract and Applied Analysis

Uniform stabilization of a coupled structural acoustic system by boundary dissipation

Mehmet Camurdan

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 3, Number 3-4 (1998), 377-400.

Dates
First available in Project Euclid: 8 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1049832732

Digital Object Identifier
doi:10.1155/S108533759800061X

Mathematical Reviews number (MathSciNet)
MR1749417

Zentralblatt MATH identifier
0966.93056

Subjects
Primary: 93C20: Systems governed by partial differential equations 35L05

Keywords
Coupled structural acoustic system uniform stabilization boundary dissipation

Citation

Camurdan, Mehmet. Uniform stabilization of a coupled structural acoustic system by boundary dissipation. Abstr. Appl. Anal. 3 (1998), no. 3-4, 377--400. doi:10.1155/S108533759800061X. https://projecteuclid.org/euclid.aaa/1049832732


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