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Wave scattering by a thin elastic plate floating on a two-layer fluid. (English) Zbl 1213.35390
Summary: The hydroelastic interaction between an incident gravity wave and a thin elastic plate floating on a two-layer fluid of finite depth is analyzed with the aid of the method of matched eigenfunction expansions. The fluid is assumed to be inviscid and incompressible. A two-dimensional problem is formulated within the framework of linear potential theory for small-amplitude waves. The fluid domain is divided into two and three regions for semi-infinite and finite plates, respectively, with the matching relations representing the continuities of the pressure and velocity. A new inner product involving two single integrals is proposed, in which the vertical eigenfunctions in the open water region of the two-layer fluid are orthogonal. Then the orthogonality of the eigenfunctions with respect to the newly defined inner product is used to obtain a set of simultaneous equations for the expansion coefficients of the velocity potentials, and the edge conditions are included as a part of the equation system. The effects of the fluid density ratio and the position of interface on the wave reflection and transmission are discussed. Numerical analysis shows that the method proposed herein is effective with a higher rate of convergence.
MSC:
35Q74PDEs in connection with mechanics of deformable solids
74J20Wave scattering (solid mechanics)
74F10Fluid-solid interactions
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction