Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A new model for acoustic-structure interaction and its exponential stability


Authors: Fariba Fahroo and Chunming Wang
Journal: Quart. Appl. Math. 57 (1999), 157-179
MSC: Primary 76Q05; Secondary 74F10, 93C20
DOI: https://doi.org/10.1090/qam/1672195
MathSciNet review: MR1672195
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Abstract: A new model for the interaction between the acoustic wave in an enclosed air cavity and the transversal motion of a flexible beam is proposed in this paper. This new boundary condition for the coupled wave and Euler-Bernoulli beam equations introduces sufficient damping of the energy of the system to gain uniform exponential stability. Careful physical justification of the boundary condition is based upon well-established theoretical results in acoustics. The estimate of the energy decay rate is obtained using a multiplier technique.


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DOI: https://doi.org/10.1090/qam/1672195
Article copyright: © Copyright 1999 American Mathematical Society


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