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Some analytical methods for fluid-structure interaction problems. (English) Zbl 0937.74022

Habault, Dominique (ed.), Fluid-structure interactions in acoustics. Wien: Springer. CISM Courses Lect. 396, 87-134 (1999).
Summary: We present a range of powerful analytical techniques which can be used to solve important model problems in structural acoustics. We start by reviewing Fourier transform techniques and far-field asymptotics applied to infinite geometries, and in particular study the sound generation by a vibrating wall and by a fluid-loaded elastic plate. Then we describe the Wiener-Hopf technique for solving two-part boundary value problems, and show in detail how it can be used to solve the classical Sommerfeld problem for diffraction by a rigid sharp edge, followed by application to a problem involving fluid loading. The Briggs-Bers method for determining the causal solution of initial-value problems is then described, which has important application, with very surprising results, to the dynamics of fluid-loaded structures in the presence of mean flow. We then move on to look at the behaviour of panels with periodically positioned inhomogeneities, and finally investigate a nonlinear problem of plate resonance.
For the entire collection see [Zbl 0922.00012].

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76Q05 Hydro- and aero-acoustics
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
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