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Interaction fluide structure en régime transitoire. (Transient compressible fluid structure interaction). (French) Zbl 0594.76071
Summary: To study vibrations in fluid structure interaction we use a combined formulation that couples the primal and dual principles. This reduces the problem to a study in conventional spectral theory and makes it possible to use computation codes developed at ONERA. Such a combined formulation can also be used to study dynamic problems and to define a computational scheme for the transient situation.
Here we study the transient elastoacoustic interaction problem. A formulation of the equations is made in the appropriate functional spaces. We prove the theorem of the existence and uniqueness of the solution by using some theoretical results obtained in previous vibration problems. This theorem justifies the ONERA computation algorithms.

76Q05 Hydro- and aero-acoustics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)