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Zbl 0663.76096
Deneuvy, A.C.
Theoretical study and optimization of a fluid-structure interaction problem. (English)
[J] RAIRO, Modélisation Math. Anal. Numér. 22, No.1, 75-92 (1988). ISSN 0764-583X

The small harmonic vibrations of an elastoacoustic coupled system are under study. A symmetric variational formulation is presented, which particularly suits the model problem. The mathematical study is derived and the existence of a real spectrum of eigenvalues is proved. Then, the problem of designing the coupled structure such as to obtain as large a gap as possible in the eigenvalues spectrum is considered, in order to avoid resonance for a wide range of external excitation frequencies. An optimally criterion method is applied, using the structure thickness distribution as a control variable.

MSC 2000:: *76Q05 Density waves (fluid mechanics)
74F10 Fluid-solid interactions
49S05 Variational principles of physics
35Q99 PDE of mathematical physics and other areas

Keywords: small harmonic vibrations; elastoacoustic coupled system; symmetric variational formulation; existence of a real spectrum of eigenvalues; resonance; external excitation frequencies

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