A new coupled-mode system of horizontal equations is presented for the hydroelastic analysis of large floating bodies or ice sheets of general, finite thickness, lying over variable bathymetry regions. The present method is based on the theory of shear deformable plates (or beams), and is derived by an enhanced representation of the elastic displacement field, containing additional elastic vertical modes and permitting shear strain and stress to vanish on both the upper and lower boundaries of the thick floating plate. This model extends existing third-order plate theories to plates and beams of general shape. The presented coupled-mode system of horizontal differential equations is obtained by means of a variational principle composed of the one-field functional of the elastodynamics in the plate region, and a pressure functional in the water region. The wave potential in the water column is represented by means of a local-mode series expansion containing an additional mode providing the appropriate correction term on the bottom boundary, when the slope is not mild. In the above sense, the proposed method extends previous approaches concerning hydroelastic problems based on thin-plate theory. The focus of this work is on the scattering of linear, coupled, hydroelastic waves propagating through an inhomogeneous sea ice environment, containing ice sheets of variable thickness and a non-mildly-sloped interface. Numerical results are presented in the simple two-dimensional case, showing that the presented approach efficiently models the hydroelastic problem and is able to provide accurate results when only a few terms are used in the expansion. Ideas for extending the proposed method to three dimensions are also discussed.
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