Characteristics of eigen-system for flexural gravity wave problems

For a class of boundary value problems associated with flexural gravity waves, characteristics of the eigen-system are analysed which are used to study the convergence of the expansion formulae in both cases of single and two layer fluids in water of finite and infinite depths. Using Green's function technique, the spectral representations of the vertical eigenfunctions are obtained which are used along with the orthogonal mode-coupling relations to prove the convergence of the expansion formulae. Using the expansion formulae flexural gravity wave scattering due to multiple articulations in the presence of compression are investigated. The problem is studied in both the cases of single-layer and two-layer fluids in finite water depth. Effects of compressive force, stiffness of the connectors, length of the elastic plates and water depth, position of interface on wave scattering by articulated plates are studied by analysing the reflection and transmission coefficients. This procedure of proving the convergence of expansion formulae is independent of water depth. The concept and methodology for dealing with wave-structure interaction problems discussed here can be generalised to deal with problems of similar nature arising in the broad area of mathematical physics and engineering.