Abstract This paper develops a comprehensive mathematical framework for modeling the coupled hydroelastic dynamics of sea-ice floes of arbitrary shape and non-uniform thickness under linear ocean wave forcing, with particular emphasis on oblique wave incidence. We simultaneously incorporate all six rigid-body motions (heave, surge, sway, roll, pitch, and yaw) and the complete spectrum of flexural deformation modes within a unified Green’s function formulation. The water flow is modeled using potential theory governed by Laplace’s equation, while the floe obeys the generalized Kirchhoff-Love plate equation with spatially varying flexural rigidity. We formulate the coupled fluid-structure interaction problem through kinematic velocity-matching conditions and dynamic pressure-continuity conditions at the ice-water interface. The submerged floe geometry is represented as a non-axisymmetric, piece-wise smooth orientable surface parameterized by a piece-wise differentiable draft function, accommodating realistic irregular features including thickness variations, keels, and submerged ridge structures. The elastic eigenproblem with free-edge boundary conditions yields a complete orthogonal basis of deformation modes, accounting for added-mass effects through modified natural frequencies. By decomposing the velocity potential into partial potentials associated with incident waves, scattered waves, rigid motions, and elastic modes, we reduce the problem to a system of Fredholm integral equations of the second kind for surface density functions on all boundary segments. We derive the complete 6 × 6 mass, added-mass, and hydrostatic stiffness matrices for floes of arbitrary geometry, enabling analysis of fully coupled dynamics. A numerical implementation is developed and validated against multiple floe geometries, including elliptical disk-cone configurations and complex asymmetric shapes with variable thickness and ice keels. Results demonstrate that oblique wave incidence excites all six rigid degrees of freedom, with significant energy exchange between rigid motions and flexural modes near resonance conditions. The Response Amplitude Operators (RAOs) reveal geometry-dependent resonance phenomena and strong coupling between modes for non-symmetric configurations. Energy budget analysis quantifies the distribution among heave, surge, sway, roll, pitch, and elastic deformation modes across the frequency spectrum.
Andrei Ludu (Fri,) studied this question.