Uniform stabilization of a coupled structural acoustic system by boundary dissipation
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 reduc...
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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | Abstract and Applied Analysis |
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| Online Access: | http://dx.doi.org/10.1155/S108533759800061X |
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| _version_ | 1832556317354491904 |
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| author | Mehmet Camurdan |
| author_facet | Mehmet Camurdan |
| author_sort | Mehmet Camurdan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1e72d2e743a64129ba7d54bc55e6ec04 |
| institution | Kabale University |
| issn | 1085-3375 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1e72d2e743a64129ba7d54bc55e6ec042025-02-03T05:45:41ZengWileyAbstract and Applied Analysis1085-33751998-01-0133-437740010.1155/S108533759800061XUniform stabilization of a coupled structural acoustic system by boundary dissipationMehmet Camurdan0Department of Applied Mathematics, University of Virginia, Thornton Hall, Charlottesville 22903, VA, USAWe 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.http://dx.doi.org/10.1155/S108533759800061XCoupled structural acoustic systemuniform stabilizationboundary dissipation. |
| spellingShingle | Mehmet Camurdan Uniform stabilization of a coupled structural acoustic system by boundary dissipation Abstract and Applied Analysis Coupled structural acoustic system uniform stabilization boundary dissipation. |
| title | Uniform stabilization of a coupled structural acoustic system by
boundary dissipation |
| title_full | Uniform stabilization of a coupled structural acoustic system by
boundary dissipation |
| title_fullStr | Uniform stabilization of a coupled structural acoustic system by
boundary dissipation |
| title_full_unstemmed | Uniform stabilization of a coupled structural acoustic system by
boundary dissipation |
| title_short | Uniform stabilization of a coupled structural acoustic system by
boundary dissipation |
| title_sort | uniform stabilization of a coupled structural acoustic system by boundary dissipation |
| topic | Coupled structural acoustic system uniform stabilization boundary dissipation. |
| url | http://dx.doi.org/10.1155/S108533759800061X |
| work_keys_str_mv | AT mehmetcamurdan uniformstabilizationofacoupledstructuralacousticsystembyboundarydissipation |