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