Some Analytical Methods for Fluid-Structure Interaction Problems
The aim of this chapter is to 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. We then 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 of 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.
KeywordsHalf Plane Pole Contribution Stop Band Fluid Loading Dispersion Function
Unable to display preview. Download preview PDF.
- Olver, P.: Asymptotics and Special Functions. Academic Press. 1974.Google Scholar
- Junger, M.C. & Feit, D: Sound, Structures, and Their Interaction. MIT Press. 1986Google Scholar
- Crighton, D.G. & limes, D.: The modes, resonances and forced response of elastic structures under heavy fluid loading. Phil. Trans. R. Soc. Lond., 312, 295–341.Google Scholar
- Briggs, R.J.: Electron-stream Interaction with Plasmas. MIT Press. 1964.Google Scholar
- Bcrs, A.: Space-time evolution of plasma instabilities — absolute and coiiveetive. In Handbook of Plasma Physics, ed M.N. Rosenbluth, R. Z. Sagdeev. 1:451–517. North-Holland. 1983.Google Scholar
- Landahl, M.T.: On the stability of a laminar incompressible boundary layer over a flexible surface. J. Fluid Mech. 13, 609 632. 1962.Google Scholar
- Cairns, H.A.: The role of negative1 energy waves in some instabilities of parallel flows. J. Fluid Mcch.. 92, 1 14. 1979.Google Scholar
- Lingwood, R.J. & Peake, N.: On the causal behaviour of flow over a compliant wall. J. Fluid Mech., to appear. 1998.Google Scholar
- Green, M.R. & Crighton, D.G.: Fluid loaded elastic plate with mean flow: point forcing and three-dimensional effects. J. Fluid Mech., submitted. 1998.Google Scholar