Modelling of Fluid/Structure Interactions
This chapter is devoted to the basic equations of Vibro-Acoustics. Only thin elastic bodies are considered.
First, the approximate equations governing the linear vibrations of thin plates, thin circular cylindrical shells and spherical shells are established. The approximation is based on the hypothesis that the elastic body has one dimension which is small compared to the other two ones and to the wavelengths of the vibrations.
Then, the theory of in vacuo thin plates and cylindrical shells under harmonic excitations is rapidly summarized (resonance mode series expansion, boundary integral representation).
The other sections deal with the response of fluid-loaded plates and shells, excited either by deterministic forces (harmonic or transient) or by random forces. The fluid load is represented by a boundary integral. Different representations of the solution are developed: boundary integral representation of the structure displacement and of the sound pressure field; fluid-loaded eigenmode series and fluid-loaded resonance mode series. These different theoretical aspects are developed on canonical examples with increasing complexity.
KeywordsCylindrical Shell Resonance Mode Boundary Integral Equation Acoustic Pressure Plate Equation
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